Algebra 2H Chapter 3 Part 1 Review

1. Use 2( ) 3 2 5f x x x= − + to answer the following questions.

a. ( 3)f − b. ( 2)f x +

c. Calculate the slope between (0) and (1)f f . d. Simplify (4 ) (4)f h f

h

+ −

2. Use 18 2

( )7 21

xh x

x

+=+

and ( ) 9 8z x x= + .

a. Write the domain of ( )h x in interval notation. b. What is the x-intercept of h(x)?

c. Write the domain of ( )z x in interval notation. d. What is the y-intercept of z(x)?

3. Use the table below to answer the questions that follow. a. What is the domain of f(x)?

b. What is the range of g(x)? c. Is f(x) a function or relation? d. Solve g(x) = 2. e. Solve f(x) = 2.

f. Evaluate f(0) + g(-4).

4. Identify the following characteristics of the graph of f(x) below.

a) Domain:

b) Range:

c) Evaluate f(4)

d) Evaluate f(1)

e) Solve f(x) = -3

f) x intercepts:

g) y intercept:

h) Interval where function is increasing

i) Interval where function is decreasing

j) Interval where function is constant

k) Points of discontinuity

x f(x) g(x)

5 8 2

0 2 1

3 -6 8

-4 2 -1

5 0 -2

5. Evaluate the following based on the piecewise function z(x) below.

2 5 , 2

( ) 3 , -2 3

18, 5

x x

z x x x

x

− < −= ≤ < <

a. z(-4) b. z(2) c. z(0) d. z(4) e. z(10)

For the graphs below, identify the domain and range and write in interval notation.

6. 7.

Domain: Domain:

Range: Range:

8. Identify the parent function, and then describe how it is transformed (be specific about shifts, reflections, stretches, or shrinks).

a. 1

| | 72

y x= − + b. 2 8y x= − + c. 3( 5) 6y x= − + +

parent: parent: parent:

d. | 2 | 10y x= − − + e. 1

4 53

y x= + f. 135 2 4

xy = ⋅ +

parent: parent: parent:

9. Write an equation based on the transformation described.

a. y x= is reflected across the y-axis and then reflected across the x-axis and then up 17 units and

then to the right 8.

b. 2xy = is shifted down 6 and then left 3 and then reflected across the x-axis and then up 6.

10. Graph the equations below.

a. 2 3xy −= − + b. 4 | 3 | 6y x= − − −

c. 2 ( 5) 6y x= − + + d. 2123( 4) 5y x= − − +