Math 1513 College Algebra - canvas.rose.edu

Math 1513 College Algebra

Unit 1: Functions and their Graphs, Ellipses and Hyperbolas

Table of Contents

Sec 2.1 and 2.2: Functions and their Graphs pages 2 - 7

Answers to 2.1 and 2.2 page 8

Sec 2.3 and 2.4: Linear Functions and Slope pages 9 - 12

Answers to 2.3 and 2.4 page 13

Sec 2.5: Transformations of Functions pages 14 - 16

Answers to 2.5 pages 17 - 18

Sec 2.6: Algebra and Composition of Functions pages 19 - 20

Answers to 2.6 page 21

Sec 2.7: Inverse Functions pages 22 - 25

Answers to 2.7 pages 26 -27

Sec 2.8: Midpoint, Distance, and Circles pages 28 - 30

Answers to 2.8 page 31

Sec 7.1 – 7.2: Ellipses and Hyperbolas pages 32 - 36

Answers to 7.1 – 7.2 page 37 - 38

Important Skills/Topics for 1513 Unit 1 Exam

Section 2.1

Find domain and range of graphs, using interval notation

Use functional notation

Find x- and y-intercepts

Use Vertical Line Test to determine if a graph is a function

Section 2.2

Identify intervals on which a function is increasing/decreasing/constant

Identify relative maxima and minima, as well as where they occur

Be able to evaluate piece-wise functions

Determine if a function is odd or even, as well as resulting symmetry

Sections 2.3 and 2.4

Identify the slope and y-int of a linear function

Graph linear functions

Write equations of lines given slope and a point

Determine if lines are parallel or perpendicular

Section 2.5

Identify all possible transformations of a given function

Graph transformed functions

Section 2.6

Compose functions

Find domain of functions, given the equation

Find inverse functions of a given function

Section 2.7

Find midpoint and distance (and know the formulas)

Circles: be able to graph, identify center/radius, and put into standard form

Sections 7.1 and 7.2

Ellipses: be able to graph, identify center/radius, and put into standard form

Hyperbolas: be able to graph, identify center/radius, and find equation of asymptotes

Page 1

Math 1513 College Algebra Name _____________________________________

Section 2.1 and 2.2 Date ______________

Unit 1: Functions and their Graphs, the Basics

1) Define the following terms:

a) Domain

b) Range

c) Function

Determine the domain and range of therelation.

2) {(-3, -4), (1, 6), (-9, -8), (4, -6),(-1, 9)}

3) {(-4, 6), (-4, -9), (9, 9), (5, -7), (8, 3)}

Tell whether the relation is a function.4) {(-2, -1), (1, -6),(5, -1), (8, -9), (11, 8)}

5) {(7, 7), (1, 7), (6, 1), (11, 6), (1, -8)}

6) What is the "Vertical Line Test"?

7) When finding domain from a graph, youlook: __________________

For range, you look: _______________

Tell whether the relation is a function. State thedomain and range using interval notation.

8)

Function?

Domain:

Range:

9)

Function?

Domain:

Range:

Page 2

10)

Function?

Domain:

Range:

Evaluate the function.11) Find f(-4) when f(x) = x2 - 2x - 2.

12) Find f(19) when f(x) = x - 13

13) Find f(0) when f(x) = x2 + 5x - 4.

Use the graph of y = f(x) to find the functionvalue.

14)

a) f(3) = b) f(-4) =

c) f(0) = d) f(4) =

Find the value(s) of x when given thevalue for f(x).

e) f(x) = 4 f) f(x) = -4

g) f(x) = 0 has how many answers?

Identify the intercepts.15)

x-intercepts:

y-intercepts:

Page 3

Section 2.2 Functions and their Graphs

16) Define the following:

A) A function is increasing whenon the open interval I, for every x2 > x1then f x2 > f x1

B) A function is decreasing when on theopen interval I, for every x2 > x1 then

f x2 < f x1

C) A function is constant whenon the open interval I, for every x1 x2then f x1 = f x2

17) When determining where a functionmight be increasing/decreasing/constant,how do you use the x- and y-values ofthe graph?

Question: Why must we use open intervalsinstead of closed?

Identify the intervals where the function is a)increasing, or b) decreasing, or c) constant.

18)

Increasing:

Decreasing:

Constant:

19)

Increasing:

Decreasing:

Constant:

Page 4


A) A function value is a relativemaximum when on the open interval I,for every x2 x1 then f x2 > f x1

B) A function is relative minimum when on the open interval I, for every x2

x1 then f x2 < f x1

21) Visually, how do you identify maxs andmins on a graph?

22) NOTE:

The max (min) value is the y-value!

Where the max (min) value occurs isthe x-value.

23) Explain the difference between a globalmax/min vs a relative max/min.

The graph of a function f is given. Use thegraph to answer the question.

24) Find the numbers, if any, at which fhas a relative maximum. What arethe relative maxima?

25) Find the numbers, if any, at which fhas a relative minimum. What arethe relative minima?

Page 5


A) A function f is an even function iffor every x, f(-x) = f(x)

Even functions are symmetric to___________

B) A function is odd function iffor every x, f(-x) = - f(x)

Odd functions are symmetric to___________

27) To determine if a function isodd/even/neither you:

Step 1:

Step 2:

Determine whether the given function is even,odd, or neither.

28) f(x) = x3 - 2x

29) f(x) = x3 + x2 + 3

30) f(x) = 2x2 + x4 - 9

31) f(x) = x3 - 5x + 7

Use possible symmetry to determine whether the graph isthe graph of an even function, an odd function, or afunction that is neither even nor odd.

32)

33)

Page 6

34)

Evaluate the piecewise function at the givenvalue of the independent variable.Tip: when dealing with peicewise functions:1) Make sure you are using the correct "functionpiece" for the given x2) Pay attention to the "transistion" x-value

35) f(x) = 3x - 2 if x < 12x + 3 if x 1

a) f(0) =

b) f(-3) =

c) f(1) =

d) f(4) =

36) g(x) =x2 + 5x + 8

if x -8

x - 1 if x = -8

; g(5)

Graph the function.37) f(x) = -x + 3 if x < 2

2x - 3 if x 2

38) f(x) = 5 if x < 1x2 if x 1

Page 7

Answer KeyTestname: 1513 FUNCTION BASICS

1) See notes and/or book section 7.62) Domain: {-9, -3, 4, -1, 1}; range: {-8, -4, -6,

9, 6}3) Domain: {-4, 5, 8, 9}; range: {-9, -7, 3, 9, 6}4) Function, since each input (x) has only one

output.5) Not a function, since the input value of 1

has two output values. (7 and -8)6) see notes and/or book section 7.67) domain: look left to right

range: look down to up8) Function

Domain: ( , )Range: ( , 5]

9) Not a functionDomain: [-1, )Range: ( , )

10) FunctionDomain: ( , )Range: ( , 3]

11) 2212) 613) -414) a) - 4 b) -2

c) 0 d) 2e) x= -3 f) x = 3g) five (each x-intercept)

15) (6, 0), (-6, 0), (0, 4), (0, -4)16) see page 230 in section 2.217) You look at the y-values (from left to right) to

determine increasing/decreasing/constant.

You use the x-values to state the intervals onwhich this occurs.

18) (-2, 2)19) (- , 3)20) see page 231 in section 2.221)22)23)24) f has a relative maximum at x = 0 : the

relative minimum is 1

25) f has a relative minimum at x = -2 and 2; the relativeminimum is 0

26) see page 231 in section 2.227)28) Odd29) Neither30) Even31) Neither32) Even33) Neither34) Odd35) 5

36) 3013

37)

38)

Page 8


Section 2.3 and 2.4 Date ______________

Unit 1: Linear Functions and Slope

1) For the exam, you must be able to:

a) Find the slope and y-intercept of aline given either the slope-interceptform or the general form.

b) Graph a line given either theslope-intercept form or the generalform.

c) Write the equation of a line given apoint on the line and the slope.

d) Identify if lines are parallel,perpindicular, or neither.

e) Find the slope of a line given twopoints.

2) Fill in the following formulas:Slope Formula

Slope-Intercept form of a line

Point-Slope form of a line

General form of a line

3) For slope, does it matter which pointyou use for Point 1 or Point 2?

For application problems, what dowe typically call slope?

4) All horizontal lines are of the form:

The slope for horz. lines is:

All vertical lines are of the form:

The slope for vert. lines is:

5) Define Parallel lines

Define Perpendicular lines

6) How do you graph a line inslope-intercept form?

In general form?

Page 9

Determine the slope and the y-intercept of thegraph of the equation.

7) 3x + 5y = -2

8) 10x - 12y - 120 = 0

9) x - 1 = 0

Find the slope of the line that goes through thegiven points.

10) (2, -3), (-7, 8)

11) (-1, 1) and ( 12

, 4)

12) (15

, 3) and ( 15

, 0)

13) (a, b), (-a, b)

Graph the equation.14) 4x + 5y - 18 = 0

15) y = 1

Graph the linear function by plotting the x-

and y-intercepts.

16) 13

x + y - 3 = 0

Page 10

17) When asked to write the equation ofa line always start with thepoint-slope form: y - y1 = m x - x1

Ques: What two pieces ofinformation do you need to write theequation of a line?

Note 1: If you are not given the slope ofthe line, finding it will be step 1.

We may give you two points,another line which is parallel/perp tothe desired line, etc.

Note 2: Make sure to read yourinstructions. You may be asked to put youranswer in point-slope, slope-intercept,and/or general form.

Note 3: When dealing with horz/vert linesit is helpful to graph the given informationfirst.

Use the given conditions to write an equationfor the line in slope-intercept form.

18) Slope = 3, passing through (3, 8)

19) Slope = 45

, passing through (2, 7)

20) Slope = 47

, y-intercept = 2

21) Passing through (1, -8) and (-7, 8)

Determine whether the lines are parallel,perpendicular, or neither.

22) 3x - 2y = 11 2x + 3y = -7

23) f(x) = 4x + 7g(x) = -4x + 3

24) 6x + 2y = 815x + 5y = 21

Page 11

Use the given conditions to write an equationfor the line in the indicated form.

25) Passing through (3, 2) and parallel tothe line whose equation is y = 2x - 6;point-slope form

26) Passing through (4, 5) andperpendicular to the line whoseequation is y = 4x + 7;point-slope form

Find an equation of the line. Graph the line.

27) Horizontal line through 14

, 0

28) Vertical line through (9, 8)

29) Perpendicular to y = 6,through (8, 11)

30) Through (-3, -9),parallel to the x-axis

Page 12

Answer KeyTestname: 1513 LINEAR FUNCTIONS

1)2)3)4)5)6)7) m = -

35

; (0, - 25

)

8) m = 56

; (0, -10)

9) m = undefined; no y-int

10) -119

11) 212) Undefined13)14)

15)

16) intercepts: (0, 3), (9, 0)

17)18) y = 3x - 1

19) y = 45

x + 275

20) f(x) = 47

x + 2

21) y = - 2x - 622) perpendicular23) neither24) parallel25) y - 2 = 2(x - 3)

26) y - 5 = -14

(x - 4)

27) y = 028) x = 929) x = 830) y = -9

Page 13


Section 2.5 Date ______________

Unit 1: Transformations of Functions

1) There are three main categories oftransformations:

1. Horizontal and Vertical Shiftswhich move the graphs left/right andup/down.

2. Reflections about the x and/or yaxes.

3. Horizontal and Vertical Shrinkingand Stretching

The key to this topic is being able to lookat a given function and determine all thetransformations which have been done.

2) General Information1. Vertical transformations act asexpected, while Horizontaltransformations work in the oppositemanner you first expect.

2. Horiztonal transformations occur"inside" the basic function, whilevertical trans. are on the "outside".

3. When there are multipletransformations, they are done inorder of Order of Operations.

4. Shifts are accomplished byadding/subtracting constants.

5. Reflections are accomplished bymultiplying by -1.

6. Shrinks/Stretchs are accomplishedby multiplying by a positive number.

Begin by graphing the standard quadraticfunction f(x) = x2 . Then use transformations ofthis graph to graph the given functions.

3) f(x) = x2 g(x) = x2 + 2

h(x) = x2 + 4 p(x) = x2 - 6

Begin by graphing the standard square rootfunction f(x) = x . Then use transformations ofthis graph to graph the given function.

4) f(x) = x g(x) = x + 2

h(x) = x + 5 p(x) = x - 6

Page 14

Begin by graphing the standard absolute valuefunction f(x) = x . Then use transformations ofthis graph to graph the given function.

5) f(x) = x g(x) = x - 4

h(x) = - x - 4 h(x) =-x - 4

Begin by graphing the square root function f(x)= x Then use transformations of this graph tograph the given function.

6) f(x) = x g(x) = 2 x

h(x) = 6 x p(x) = 13

x

Begin by graphing the standard function f(x) =x3 Then use transformations of this graph tograph the given function.

7) f(x) = (x)3 g(x) = (2x)3

h(x) = (5x)3 p(x) = (12

x)3

Begin by graphing the standard quadraticfunction f(x) = x2 . Then use transformations ofthis graph to graph the given function.

8) f(x) = x2

h(x) = (x - 3)2 + 4

First, state (in order) whichtransformations are occuring.

Page 15

Begin by graphing the standard square rootfunction f(x) = x . Then use transformations ofthis graph to graph the given function.

9) f(x) = xg(x) = 5 -x + 2 - 1


Begin by graphing the standard absolute valuefunction f(x) = x . Then use transformations ofthis graph to graph the given function.

10) g(x) = - 3x - 2 + 5


Use the graph of y = f(x) to graph the givenfunction g.

11) g(x) = -2f(x)


Use the graph of the function f, plotted with asolid line, to sketch the graph of the givenfunction g.

12) g(x) = f(x + 1) + 2

y = f(x)


Page 16

Answer KeyTestname: 1513 TRANSFORMATIONS

1)2)3)

4)

5)

6)

7)

8)

Page 17

Answer KeyTestname: 1513 TRANSFORMATIONS

9)

10)

11)

12)

Page 18


Section 2.6 Date ______________ Unit 1: Combinations and Composite Functions

1) When finding domain of a singlefunction, remember two things: wecan't divide by zero and we don'ttake the square root of a negativenumber.

Find the domain of the function.

2) g(x) = 2xx2 - 36

3) f(x) = x2

x2 + 5

4) f(x) = 24 - x

5) The Algebra of Functions worksexactly as you expectadding/subtracting/mult/divide towork.

be careful with negatives whensubtracting and simplifying whendividing

When finding the domain of combinedfunctions, take the most restrictivedomain. Use interval notation fordomain.

Given functions f and g, perform the indicatedoperations and find the domain of thecombined function.

6) f(x) = 9x2 - 5x, g(x) = x2 - 3x - 10

Find fg

.

domain:

7) f(x) = 4 - 5x, g(x) = -8x + 5

Find g - f.

Domain:

8) Find the domain of (fg)(x) when f(x)= 5x + 3 and g(x) = 3x - 7.

(fg)(x)=

domain =

Page 19

9) Composition of Functions is atwo-step process: Work with the"inside function" and take thatanswer as the input for the "outside"function.

(f g)(x) = (f(g(x)) and (g f)(x) =(g(f(x))

For the domain of the compositefunction, you must look at both thedomain restrictions of the "inside"function and the domain of thecomposed function.

For the given functions f and g , find theindicated composition.

10) f(x) = 14x2 - 10x, g(x) = 7x - 8(f g)(9)

11) f(x) = x2 - 2x - 5, g(x) = x2 + 2x + 2(f g)(-4)

12) f(x) = x - 104

, g(x) = 4x + 10

(g f)(x)

13) f(x) = 6x - 3

, g(x) = 47x

(f g)(x)

Find the domain of the composite function f g.14) f(x) = x; g(x) = 3x + 9

15) f(x) = 8x + 8

, g(x) = 8x

16) When looking for the functions thatresult in the composition, look for a"natural" "inside" function.

hint: for the outside function, replacethe inside function with ( ). Once youfind that, replace the ( ) with x.

Find functions f and g so that h(x) = (f g)(x).17) h(x) = |6x + 8|

18) h(x) = 1x2 - 6

19) h(x) = 1x2

+ 4

Page 20

Answer KeyTestname: 1513 FUNCTION ALGEBRA

1)2) (- , -6) (-6, 6) (6, )3) (- , )4) (- , 24]5)

6) 9x2 - 5xx2 - 3x - 10domain: ( , -2) (-2, 5) (5, )

7) -3x +1Domain: ( , )

8) (fg)(x) = ( 5x + 3 )( 3x - 7)

Domain: 73

,

9)10) 41,80011) 7512) x

13) 42x4 - 21x

14) [-3, )15) (- , -1) or (-1, 0) or (0, )16)17) f(x) = |x|, g(x) = 6x + 818) f(x) = 1/x, g(x) = x2 - 619) f(x) = x + 4, g(x) = 1/x2

Page 21


Sec 2.7 Date ______________

Unit 1: Inverse Functions

1) Describe what "inverse function"means.

Graphically, you can tell a function hasan inverse if it is a one-to-one function.

This means that1) the graph is a function, ie. passes thevertical line test (each x has only one y)and 2) passes the horizontal line test(each y has only one x).

Does the graph represent a function that has aninverse function?

2)

3)

4)

5) To graphically find the inverse of afunction, you reflect it about the liney = x

note: This means each point will swap itsx and y values.

Use the graph of f to draw the graph of itsinverse function.

6)

Page 22

Use the graph of f to draw the graph of itsinverse function.

7)

8)

9) Notation

The inverse function of f(x) is denoted byf-1(x) or sometimes just f-1

In this case, the -1 is not to be confused

with an exponent of -1, such as x-1 = 1x

10) Two functions are inverses of eachother if and only if:

f g (x) = x and g f (x) = x

Review: For the given functions f and g , findthe indicated composition.

11) f(x) = 5x + 15, g(x) = 5x - 1

(f g)(x)

Determine which two functions are inverses ofeach other.

12) f(x) = 3x g(x) = x3

h(x) = 3x

13) f(x) = x - 32

g(x) = 2x - 3

h(x) = x + 32

Page 23

14) f(x) = x3 - 11 g(x) =3

x - 11

h(x) = x3 + 11

15) To find the inverse function of f(x):

step 1: Rewrite f(x) = as y =

step 2: Swap all x's with y's and viceversanote: at this point you actually have the inverse

Step 3: Solve the new equation for y =

Step 4: Rewrite y = as f-1(x) =

Find the inverse of the one-to-one function.16) f(x) = -8x + 8

17) f(x) = 73x - 1

18) f(x) = (x + 6)3

19) f(x) = x - 8

Graph f as a solid line and f-1 as a dashed linein the same rectangular coordinate space.

Use interval notation to give the domain andrange of f and f-1.

20) f(x) = 3x - 1

Page 24

Graph f as a solid line and f-1 as a dashed linein the same rectangular coordinate space.

Use interval notation to give the domain andrange of f and f-1.

21) f(x) = x3 - 6

22) f(x) = x2 - 1, x 0

Page 25

Answer KeyTestname: 1513 INVERSE FUNCTIONS

1)2) No3) Yes4) No5)6)

7)

8)

9)10)11) 25x + 1012) f(x) and g(x)13) g(x) and h(x)14) g(x) and h(x)

15)16) f-1(x) = x - 8

-8

17) f-1(x) = 73x

+13

18) f-1(x) =3

x - 619) f-1(x) = x2 + 820)

f domain = (- , ); range = (- , )f-1 domain = (- , ); range = (- , )

21)

f domain = (- , ); range = (- , )f-1 domain = (- , ); range = (- , )

Page 26

Answer KeyTestname: 1513 INVERSE FUNCTIONS

22)

f domain = (0, ); range = (-1, )f-1 domain = (0, ); range = (-1, )

Page 27


Section 2.8 Date ______________ Unit 1: Midpoint, Distance, and Circles

Midpoint1) What is the formula to find the

midpoint between two points?

note: the midpoint is just the averagex-value and the average y-value

Find the midpoint of the line segment whoseend points are given.

2) (5, -4) and (7, -1)

3) (2, - 3) and ( 32

, - 1)

4) (5 3, 9 6) and (8 3, 12 6)

Distance5) What is the formula to find the

distance between two points?

note: the distance formula is anapplication of Pythagorean's Thm

Find the distance between the pair of points.6) (7, 3) and (-2, -7)

7) (4, -4) and (-3, -5)

8) (-2 5, -3) and (2 5, -2)

Page 28

Circles9) What is the Standard Form of the

Equation of a Circle?

When in this form, where is the center?

Note: when writing the equation of a circle,you may have to Complete the Square

Write the standard form of the equation of thecircle with the given center and radius.

10) (-8, 8); 5

11) center = origin; 14

12) (10, 0); 1

Find the center and the radius of the circle.13) (x + 2)2 + (y - 6)2 = 81

Graph the equation and state its domain andrange. Use interval notation

14) x2 + y + 3 2 = 49

Center:

Domain:

Range:

Graph the equation. State its domain and range15) (x - 1)2 + (y - 3)2 = 36

Center:

Domain:

Range:

16) Question: How do you graph acircle on a graphing calculator?

Page 29

Complete the square and write the equation instandard form. Then give the center and radiusof the circle and graph the circle.

17) 6x2 + 6y2 = 36

18) x2 + 14x + 49 + y2 - 14y + 49 = 49

19) x2 + y2 + 4x + 10y = 7

20) Visually, what is the differencebetween a circle and an ellipse?

Page 30

Answer KeyTestname: 1513 MIDPT, DISTANCE, CIRCLES

1)2) (6, - 5

2)

3) ( 74

, - 2)

4) (13 32

, 21 62

)

5)6) 1817) 5 28) 99)

10) (x + 8)2 + (y - 8)2 = 2511) x2 + y2 = 1412) (x - 10)2 + y2 = 113) (-2, 6), r = 914)

Domain = (-7, 7); Range = (-7, 7)15)

Domain = (-5, 7), Range = (-3, 9)16)17) x2 + y2 = 6

(0, 0), r = 6

18) (x + 7)2 + (y - 7)2 = 49(-7, 7), r = 7

19) (x + 2)2 + (y + 5)2 = 36(-2, -5), r = 6

20)

Page 31


Section 7.1 and 7.2 Date ______________

Unit 1 - 6: Ellipses and Hyperbolas

1) What is the Standard Form of theEquation of an Ellipse?

When in this form, where is thecenter?

What are the "major axis" and "minoraxis"? How do you know which isthe major (or minor) axis?

note: The textbook always uses "a" forthe major axis and "b" for the minor.Rather than memorize two differentforms, just remember the value under xgoes with x and the value under y goeswith y...

How do you find the vertices of anellipse?

note: We will not be discussing the fociof ellispes or hyperbolas.

Graph the ellipse.

2) x249

+y225

= 1

Step 1: state the center of the ellipse

Step 2: Is this a vertical or horizontalellipse? Why?

Step 3: What is the radius in thex-direction?

in the y-direction?

Step 4: Graph the ellipse, starting withthe center...

Graph the ellipse.

Page 32

3) 4x2 = 64 - 16y2

Can you graph this as is??

So now...

State the center of the ellipse:

The radius in the x-direction is _____

The radius in the y directions is ______

Find the standard form of the equation of theellipse.

4)

5)

Page 33

Graph the ellipse.

6) (x + 1)216

+(y - 2)2

9= 1

Center:

x-radius:

y-radius:

7) 16(x + 2)2 + 4(y - 2)2 = 64

Center:

x-radius:

y-radius:

Convert the equation to the standard form foran ellipse by completing the square on x and y.

8) 4x2 + 36y2 - 16x + 72y - 92 = 0

9) 36x2 + 4y2 - 72x + 16y - 92 = 0

Page 34

Sec 7.2 Hyperbolas10) The standard forms of hyperbolas

are:(x - h)2

a2-

(y - k)2

b2= 1

and

(y - k)2

a2-

(x - h)2

b2= 1

Which form is for thehorizontal-opening hyperbola?

What information do these forms tellus?

note: Again, rather than remember twodifferent forms, just remember the valueunder x determines the distance you movein the x direction from the center and thevalue under y goes with y...

Asymptotes: These are the lines drawnthrough the corners of the box createdfrom the foci.

y - k = ± riserun

(x - h) (where the rise

and run come from the a and b's...)

Use the center, vertices, and asymptotes tograph the hyperbola.

11) x24

-y236

= 1

Center:

Horizontal or Vertical?

x-radius =

y-radius =

12) (y + 2)29

-(x - 1)2

16= 1

Center:


x-radius =

y-radius =

Page 35

13) 36y2 - 4x2 = 144

Standard form =

Center:


x-radius =

y-radius =

Asymptote equations:

14) (x - 1)2 - 4(y - 2)2 = 4

Standard form =

Center:


x-radius =

y-radius =

Asymptote equations:

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Answer KeyTestname: 1513 ELLIPSES AND HYPERBOLAS

1)2)

3)

4) x24

+y216

= 1

5) x281

+y24

= 1

6)

7)

8) (x - 2)236

+(y + 1)2

4= 1

9) (x - 1)24

+(y + 2)2

36= 1

10)11) Asymptotes: y = ± 3x

12)

Page 37

Answer KeyTestname: 1513 ELLIPSES AND HYPERBOLAS

13) Asymptotes: y = ±13

x

14)

Page 38

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Math 1513 College Algebra - canvas.rose.edu