Unit 1B Review (Algebra 2)

Unit 1B Review

​Algebra 2

​Sections in Unit 1B

• 1B.1 Graphing Function Families (Absolute Value)

• 1B.2 Inverse Functions

• 1B.3 Operations on Functions

• 1B.4 Composition of Functions

• 1B.5 Composition Applications

Multiple Choice

Describe the transformations from the parent function giving the following:

$$f\left(x\right)=\left|x+3\right|-5$$  

• Shift left 5, down 3

• Shift left 3, down 5

• Shift right 5, up 3

• Shift right 3, down 5

Multiple Choice

Describe the transformations from the parent function giving the following:

$$f\left(x\right)=\frac{1}{3}\left|x-4\right|$$  

• Vertical shrink by 1/3, shift right 4

• Vertical stretch by 3, shift left 4

• Vertical stretch by 3, shift right 4

• Vertical shrink by 1/3, shift left 4

Multiple Choice

Select the correct function for the graph:

• $$f\left(x\right)=\left|x-2\right|+1$$  

• $$f\left(x\right)\left|x-1\right|+2$$  

• $$f\left(x\right)=\left|x+1\right|+2$$  

• $$f\left(x\right)=\left|x+2\right|-1$$  

Multiple Choice

Select the correct function for the graph:

• $$f\left(x\right)=\frac{1}{3}\left|x-7\right|$$  

• $$f\left(x\right)=\frac{1}{3}\left|x\right|-7$$  

• $$f\left(x\right)=3\left|x+7\right|$$  

• $$f\left(x\right)=3\left|x\right|-7$$  

Multiple Choice

Find the inverse of the following:

$$\left\{\left(-1,0\right),\ \left(3,4\right),\ \left(5,\ -10\right)\right\}$$  

• $$\left\{\left(0,1\right),\ \left(-4,\ -3\right),\ \left(10,-5\right)\right\}$$  

• $$\left\{\left(1,0\right),\ \left(-3,\ -4\right),\ \left(-5,\ 10\right)\right\}$$  

• $$\left\{\left(0,-1\right),\ \left(4,3\right),\ \left(-10,5\right)\right\}$$  

Multiple Choice

If a function is graphed with its inverse, then the images will be _________ over the line $$y=x$$  .

• rotated

• reflected

• translated

• dilated

Multiple Choice

Which of these graphs does NOT show inverse functions?

Multiple Choice

Find the inverse of $$f\left(x\right)=\frac{1}{2}x+3$$  .

• $$f^{-1}\left(x\right)=-\frac{1}{2}x-3$$  

• $$f^{-1}\left(x\right)=2x-6$$  

• $$f^{-1}\left(x\right)=\frac{1}{2}y-3$$  

• $$f^{-1}\left(x\right)=2x+3$$  

Multiple Choice

Let $$f\left(x\right)=x+4$$  and $$g\left(x\right)=3x-2$$  .

Find $$\left(f-g\right)\left(x\right)$$  .

• $$\left(f-g\right)\left(x\right)=4x+2$$  

• $$\left(f-g\right)\left(x\right)=2x-6$$  

• $$\left(f-g\right)\left(x\right)=-2x+6$$  

• $$\left(f-g\right)\left(x\right)=x-4$$  

Multiple Choice

Let $$f\left(x\right)=x+4$$  and $$g\left(x\right)=3x-2$$  .

Find $$\left(f\cdot g\right)\left(x\right)$$  .

• $$\left(f\cdot g\right)\left(x\right)=3x^2+10x-8$$  

•   $$\left(f\cdot g\right)\left(x\right)=x^2-7x+10$$  

• $$\left(f\cdot g\right)\left(x\right)=3x^2+14x+8$$  

• $$\left(f\cdot g\right)\left(x\right)=-2x^2-7x+1$$  

Fill in the Blanks

Using the table, find $g\left(f\left(-1\right)\right)$  .

Fill in the Blanks

If $f\left(x\right)=-4x$   and $g\left(x\right)=x+7$  , find $f\ \left(g\left(-3\right)\right)$  .

Multiple Choice

Let $$f\left(x\right)=x^2+1$$   and $$g\left(x\right)=-7x+2$$  . Find $$\left(g\ ∘\ f\right)\left(x\right)$$  .

• $$\left(g\ ∘\ f\right)\left(x\right)=-7x^2-5$$  

• $$\left(g\ ∘\ f\right)\left(x\right)=3x^2-5$$  

• $$\left(g\ ∘\ f\right)\left(x\right)=49x^2-28x+6$$  

​That's it!

• Retry the practice version of this in Canvas as much as you'd like!

• This has similar questions to the test (without open response).