Analyzing and Inverses Test Review

You will not have your notes for you test, so you need to familiar with these words and their meaning. ​

• Domain/Range

• Increasing/Decreasing

• Positive/Negative

• End Behavior

• ​Intercepts

• Tr​ansformations

​What will be on your test tomorrow:

****There will only 3 inverse questions on the test, and the warmup for today was very similar to the questions you will see.****

1. Domain

2. Range

3. Increasing

4. Decreasing

5. Positive

6. Negative

7. End Behavior

8. Intercepts (x and y)

9. Vertical transformations

10. Horizontal transformations​

11. Relative/Absolute Max and Min​

​

​On the vocab paper I gave you, you are going to give definitions for ALL of the following words

​

Match

Match the following

• Domain

• Range

• Increasing

• Decreasing

• Positive

all x-values

all y-values

where the graph is rising (from left to right)

where the graph is falling (from left to right)

Above the x-axis

• all x-values

• all y-values

• where the graph is rising (from left to right)

• where the graph is falling (from left to right)

• Above the x-axis

Match

Match the following

• End Behavior

• Vertical Transformations

• Horizontal Transformations

• Inverses

• Negative

describes the behavior of the graph of the function at the ends of the graph

All transformations outside the function

All transformations inside the function

Swapping x and y values

below the x-axis

• describes the behavior of the graph of the function at the ends of the graph

• All transformations outside the function

• All transformations inside the function

• Swapping x and y values

• below the x-axis

Multiple Choice

How does the 5 affect the graph?

$$y=\left|5\left(x-1\right)\right|$$  

• Vertical Stretch by factor of 5

• Vertical compression by factor of 1/5

• Horizontal compression by factor of 1/5

• Horizontal compression by factor of 5

1. Domain

2. Range

3. Increasing

4. Decreasing

5. How many x-intercepts?

6. Is (-2,0) a relative or absolute minimum?

​

For this graph, give the following information

​

1. Domain: (-inf, inf) or R

2. Range: [0, inf)

3. Increasing: (-2, inf)

4. Decreasing: (-inf, -2)

5. How many x-intercepts? 1

6. Is (-2,0) a relative or absolute minimum? absolute

​

Answers:​

​

1. Positive Interval (-1, 0) (1.5, inf)

2. Negative Interval (-inf, -1) (0, 1.5)

3. True or False: The graph has 2 x-intercepts. False

4. Is the interval (-.5, 0) increasing or decreasing? Decreasing

For this graph, give the following information

​

Multiple Choice

$$-\frac{1}{2}\left(x-1\right)^2+3$$  

How does the negative affect the function?

• reflection across y-axis

• reflection across x-axis

Multiple Choice

$$-\frac{1}{2}\left(x-1\right)^2+3$$  

How does the 1/2 affect the function?

• horizontal compression

• vertical compression

• horizontal stretch

• vertical stretch

Multiple Choice

$$-\frac{1}{2}\left(x-1\right)^2+3$$  

How does the 1 affect the function?

• left 1

• up 1

• right 1

• down 1

Multiple Choice

$$-\frac{1}{2}\left(x-1\right)^2+3$$  

How does the 3 affect the function?

• left 3

• up 3

• right 3

• down 3

Multiple Choice

Zeros is another name for....

• domain

• range

• x-intercepts

• y-intercepts

Multiple Choice

Which graph has the end behavior $$As\ x\rightarrow\infty,\ y\rightarrow\infty$$  

Multiple Choice

Which graph has zeros at -2, 1, and 3? 

Fill in the Blanks

If $f\left(x\right)=\frac{1}{3}x-1$  , what is $f^{-1}\left(2\right)$  

Multiple Choice

If f(x) has the points (3,4), (-6,2) and (0,9), which would be a correct inverse point?

• (-3,-4)

• (2,-6)

• (-9,0)

• (1,2)