Review 1

Domain and Range

100

What is the domain of a quadratic function?

All real numbers or (-inf, inf)

200

Find the domain and range of the relation

{(11,13), (-24,-17), (18,0), (-1,-16), (-5,-1)}

Domain: {-24,-5, -1, 11, 18}

Range: {-17, -16, -1, 0, 13}

300

Find the domain of sqrt(2x-40)

[20, inf)

400

Find the domain of 1/((x-3)(x-2))

All real numbers except 2 and 3

500

Use the graph to find its domain and range. Write it in interval notation.

Domain: (-6,5]

Range: [-2,3)

Combine and Compose Functions

100

Given the following functions, find (f+g)(x)

f(x)=2x+1

g(x)=4x-3

6x-2

200

Given the following functions, find g(x)-f(x)

f(x)=-3x+5

g(x)=5x+3

8x-2

300

Given the following functions, find (f(x))(g(x))

f(x)=3x²+x-3

g(x)=x+5

3x³+16x²+2x-15

400

Given the following functions, find g(f(2))

f(x)=4x-4

g(x)=6x+2

26

500

Given the following table of values, find f(g(4))

12

Transformations of Functions

100

Draw the following parent functions

1. f(x)=x²

2.g(x)=x³

3.h(x)=|x|

4.m(x)=sqrt(x)

1. "U" shape

2. "S" shape

3. "V" shape

4. Curve starting at origin

200

Describe the transformation from the parent function to f(x)=(-x)³+2

Reflected across the y-axis and shifted 2 units up

300

Give me a value of a that would compress the graph of the function f(x)=a(x-2)²+4

Any value between 0 and 1

0<a<1

400

Describe the transformations that would need to take place to go from f(x)=-1/2(x+1)²-3 back to f(x)=x²

Reflect over the x-axis, stretch by a factor of 1/2, shift 1 unit right and 3 units up.

500

The parent function x⁴ was reflected over the y-axis, shifted 4 units left and 5 units down. What does that new function look like?

f(x)=(-x+4)⁴-5

Absolute Value and Piecewise Functions

100

Find the solutions of 11|x+3|+9=10

x=-32/11 and x=-34/11

200

Given the following piecewise function, evaluate f(2)

9

300

Given the following piecewise function, evaluate f(0)

3

400

Graph the piecewise function given

*answer on board*

500

Graph the piecewise function given

*answer on board*

Inverse Functions

100

Consider the function f, which is a one-to-one function with values f(8)=-2 and f(-1)=3. What values must be true for the inverse function?

f^-1(-2)=8 and f^-1(3)=-1

200

You want to restrict the domain of the function f(x)=|x-2| to make it one-to-one so that it will have an inverse. What are the largest domains, in interval notation, that you could use? 

(-inf,2) and (2,inf)

300

Use the following table of values for the one-to-one function g(x) to find g^-1(-11)

-6

400

Give me a point on the graph of the inverse of the function which slope can be found using the following formula:

(7-2)/(3-4)

(2,4) or (7,3)

500

Find the inverse of g(x)=(-x/10)+(7/10)

-10x+7