Chapter 4 Review

Pre-Calculus

Match the graph of a quadratic function with

it’s equation below:

f(x) = x2 f(x) = -(x+2)2+4 f(x) = (x+2)2-1

Describe the end behavior of the graph

of each given graph.

Use the Leading Coefficient Test to determine the end behavior of

the graph of the given polynomial function.

1.) f(x) = -x3 + 4x 2.) f(x) = x4 – 5x2 +4

3.) f(x) = x5 - x

5.) f(x) = -2x4 + 2x2

4.) f(x) = x3 – x2 - 2x

Rise Left, fall right Rise left, rise right

Fall left, rise right Fall left, rise right

Fall left, fall right

Determine without graphing, the critical

points of each function.

1.) f(x) = (x + 2)2 - 3 2.) f(x) = -x2 + 6x - 8

Min (-2,-3) Max (3,1)

3.) f(x) = 3x3 - 9x + 5 4.) = x3 + 6x2 + 5x

Min (-.47, -1.13)Max (-3.53, 13.12)Pt. of Inflection (-2,6)

Min ( 1, -1)Max (-1, 11)Pt. of Inflection ( 0 , 5)

5.) f(x) = x4 - 10x2 + 9Min ( -√5, -16)Max (0, 9)Min ( √5 , -16)

f’(x) = 2x + 4 f’(x) = -2x + 6

f’(x) = 9x2 - 9 f’’(x) = 18x

Find the zeros of each polynomial

function.

1.) x2 – 40 = 0 2.) x3 + 4x2 + 4x = 0

3.) x2 + 11x – 102 = 04.) x2 + ¾x + ⅛ = 0

x = 0, -2, -2

x = -17, 6 x = -½, -¼

If you can’t figure it out then use Quadratic Formula

Find the zeros of the polynomial function by factoring.

1.) f(x) = x3 + 5x2 – 9x - 451.) f(x) = x3 + 4x2 – 25x - 100

x = 5, -5, -4

Which of the following is a rational

zero of

f(x) = –2x5 + 6x4 + 10x3 – 6x2 – 9x

+ 4 1, -3, -2, 4, -1 ????

Remember you could use synthetic division or just do p(x) and see if you get a remainder of ZERO

= 0

So 4 is a factor, the others are not

OR

Use synthetic division to divide x4 + x3 – 11x2 – 5x +

30 by x - 2 . Then divide by x + 3 Use the result to find

all zeros of f(x).

x2 x C RSo you are left with: x2 - 5

Then all the zeroes are: -3, , 2

List all possible rational zeros of

1.) 2.)

List all possible rational roots, use synthetic division to

find an actual root, then use this root to solve the

equation.

f(x) = 2x4 + x3 – 31x2 – 26x + 24

Hint 4 and -3/2 are roots

2x2 + 6x – 4

USE QUADRATIC FORMULA!!!

Find the number of possible

positive, negative, and imaginary

zeros of: 2,0 positive roots

0 negative roots

P N IP N I

P N IP N I

2

0

0

0

0

2

1 positive root

3,1 negative roots

1

1

3

1

0

2

3,1 positive roots

1 positive root3

1

1

1

0

2

3,1 positive roots

2,0 positive roots

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Use the given root to find the

solution set of the polynomial

equation.p(x) = x4 + x3 – 7x2 – x + 6GIVEN -3 IS A ROOT

Then we can find the rest by factoring:

So the roots are:-3, -1, 1, and 2

Which equation represents the graph of

the function? f(x) = 2x2+2x-1f(x) = -x2-3x+4 f(x) = x2+10x-1

Approximate the real zeros of each

function.

0.7, -0.7 -2.5

2.3 -0.4 and -2.6

Use the given root to find the

solution set of the polynomial

equations

2i 3-iSince 2i is a root, so is -2i

Turn the roots into factors, multiply them together, then use long division

Then factor to find the remaining roots

So the roots are: 2i, -2i, 3, and -4

Since 3-i is a root, so is 3+i

Turn the roots into factors, multiply them together, then use long division

Then factor to find the remaining roots

So the roots are: 3-i, 3+I, 1, and -4

Find the vertical asymptotes, if any, of the graph of each

function.

x = -2, x = 2 x = 4

No vertical asymptote x = -7

Find the horizontal asymptote, if any, of the

graph of

y = 0y = 1

y = 1y = 3x + 3

If a monomial is on bottom then you just break it up.

Otherwise must do long division

Choose the correct graph for the rational

function