Quiz about Major Assessment #1: Functions Overview

Question 1

What is the effect of the transformation f(x) = -2 * g(x) on the graph of the function g(x)?

Accepted Answer

Vertical stretch by a factor of 2 and reflection in the x-axis

Answer

Vertical compression by a factor of 2 and reflection in the x-axis

Answer

Vertical stretch by a factor of 2 and reflection in the y-axis

Answer

Vertical compression by a factor of 2 and reflection in the y-axis

Question 2

If h(x) = 1/4 * f(x), how is the graph of h(x) related to the graph of f(x)?

Accepted Answer

It is vertically compressed by a factor of 4

Answer

It is horizontally stretched by a factor of 4

Answer

It is horizontally compressed by a factor of 4

Answer

It is vertically stretched by a factor of 4

Question 3

The function f(x) = (x - 2)² + 5 is a transformation of the parent function g(x) = x².

Describe the transformation.

Accepted Answer

Shifted 2 units to the right and 5 units up

Answer

Shifted 2 units to the left and 5 units up

Answer

Shifted 2 units to the right and 5 units down

Answer

Shifted 2 units to the left and 5 units down

Question 4

What is the effect of the transformation f(x) = g(x + 4) - 1 on the graph of the function g(x)?

Accepted Answer

Shifted 4 units to the left and 1 unit down

Answer

Shifted 4 units to the left and 1 unit up

Answer

Shifted 4 units to the right and 1 unit up

Answer

Shifted 4 units to the right and 1 unit down

Question 5

If the graph of f(x) = |x| is reflected over the x-axis, what is the new equation?

Accepted Answer

f(x) = -|x|

Answer

f(x) = |x|

Answer

f(x) = |x| + 1

Answer

f(x) = -|x| - 1

Question 6

What is the result of the transformation f(x) = 3 * g(x - 2) on the graph of the function g(x)?

Accepted Answer

Stretched vertically by a factor of 3 and shifted 2 units to the right

Answer

Stretched vertically by a factor of 3 and shifted 2 units to the left

Answer

Compressed vertically by a factor of 3 and shifted 2 units to the right

Answer

Compressed vertically by a factor of 3 and shifted 2 units to the left

Question 7

The function f(x) = -|x| has undergone which of the following transformations compared to the parent function g(x) = |x|?

Accepted Answer

Reflected over the x-axis

Answer

Reflected over the y-axis

Answer

Reflected over both the x-axis and y-axis

Answer

No transformation has occurred

Question 8

The graph of y = f(x) is vertically compressed by a factor of 6, and reflected in the x-axis. What is the equation of the image graph in terms of f?

Accepted Answer

Question 9

The shape of a roof is modeled by a transformation of the absolute value function,

f (x) = | x |. The function is reflected in the x-axis, and translated 8 units up and 10 units to the right to create the roof model.

Which equation represents the model for the roof, r(x)?

Accepted Answer

r(x) = -|x - 10| + 8

Answer

r(x) = |x + 10| + 8

Answer

r(x) = |x + 8| - 10

Answer

r(x) = -|x - 8| + 10

Question 10

Which of the following is the graph of the function $$f\left(x\right)=-2\sqrt[]{3\left(x-1\right)}+5$$ ?

[The parent function is dotted]

Accepted Answer

Question 11

Which of the following is the equation for the graph shown?

Accepted Answer

Question 12

Which of the following is the graph of the function $$f\left(x\right)=\frac{2}{x-4}+5$$ ? (The parent function is dotted.)

Accepted Answer

Question 13

In a piecewise function, every interval of the domain has its own separate function.

Accepted Answer

TRUE

Answer

FALSE

Question 14

The point (0,0) is always on the graph of a parent function.

Accepted Answer

FALSE

Answer

TRUE

Question 15

A linear equation is an example of a parent function.

Accepted Answer

TRUE

Answer

FALSE

Question 16

The shape of a roof is modeled by a transformation of the absolute value function,

f (x) = | x |. The function is reflected in the x-axis, and translated 8 units up and 10 units to the right to create the roof model.

What is the bottom width of the model roof, if each unit represents one foot?
[hint: draw completely the graph on your graphing paper]

Accepted Answer

16 feet

Answer

10 feet

Answer

18 feet

Answer

20 feet

Question 17

In graphing a piecewise function, the graph must be continuous without any breaks or holes.

Accepted Answer

FALSE

Answer

TRUE

Question 18

A piecewise function can be defined by more than two functions.

Accepted Answer

TRUE

Answer

FALSE

Question 19

A parking garage charges 5 for the first two hours and then 2 for each additional hour. Calculate the cost for parking 7 hours.

Accepted Answer

$15

Answer

$17

Answer

$19

Answer

$21

Question 20

A taxi company charges a flat rate of 4 for the first mile and then 2 for each additional mile. Write this as a piecewise function and identify the cost for a 5-mile trip.

Accepted Answer

$12

Answer

$14

Answer

$10

Answer

$8

Question 21

Use these tables. What is the value of $$f(g(0))$$ ?

Accepted Answer

4

Answer

1

Answer

-1

Answer

-2

Question 22

The set of values in the domain and range for a function are the same

Accepted Answer

Sometimes True

Answer

Always True

Answer

Never True

Question 23

Ordered pairs that satisfy a functional relationship appear as (x, f(x)).

Accepted Answer

Always True

Answer

Sometimes True

Answer

Never True

Question 24

A function graph has a vertex point.

Accepted Answer

Sometimes True

Answer

Always True

Answer

Never True

Question 25

A translation is a transformation that moves all the points of the original figure the same distance in the same direction

Accepted Answer

Always True

Answer

Sometimes True

Answer

Never True

Question 26

Which of the three functions shown above has the largest and smallest average rate of change on the interval [-3,0]?

Accepted Answer

largest g (x);

smallest m (x)

Answer

largest f (x);

smallest m (x)

Answer

largest m (x); smallest g (x)

Answer

largest g (x);

smallest f (x)

Question 27

When driving a car, an unsuspected hazard appears in the roadway. The table at the right shows the "total" stopping distance which is the sum of the "thinking" distance and the actual "braking" distance.
What is the average rate of change in the total stopping distance (feet/mph) between one car traveling 40 mph and one traveling 60 mph?

Accepted Answer

6 ft/mph

Answer

60 ft/mph

Answer

10 ft/mph

Answer

120 ft/mph

Question 28

The graph of a straight line is shown below.
Which of the statements are true in relation to the statement:
"The average rate of change is ...."

[check all that apply]

Accepted Answer

negative

Accepted Answer

constant

[means fixed]

Accepted Answer

-1 on interval [-2,0]

Answer

positive

Answer

1 on interval [1,4]

Question 29

Which of the following statements is TRUE regarding functions

f (x) and g(x) shown?

Accepted Answer

f (x) has a greater rate of change than g(x).

Answer

g(x) has a greater rate of change than f (x).

Answer

Both functions have the same rate of change.

Answer

There is insufficient information to determine the rate of change.

Question 30

Which choice describes the end behavior for the graph shown?

Accepted Answer

Question 31

According to the United States Postal Service (in 2014), first-class letters are weighed and priced as shown in the given chart.

Which of the following graphs correctly displays this information regarding the pricing of first-class letters?

Accepted Answer

Question 32

The graph at the right is a transformation of the absolute value function, f (x) = | x |.

Which of the following equations represents this graph?

Accepted Answer

f (x) = | x + 3 | - 4

Answer

f (x) = | x - 3 | - 4

Answer

f (x) = | x + 4 | - 3

Answer

f (x) = | x - 4 | - 3

Question 33

The sales s, in thousands, of a new record album increases steadily for a while and then decreases just as quickly. This information is at the given graph.

What type of graph is being used to present this information?

Accepted Answer

absolute value

Answer

quadratic

Answer

linear

Answer

exponential

Question 34

The sales s, in thousands, of a new record album increases steadily for a while and then decreases just as quickly. This information is at the given graph.

What is the average rate of change in the album sales during the first two weeks?

Accepted Answer

2,000 albums per week

Answer

1,000 albums per week

Answer

3,000 albums per week

Answer

4,000 albums per week

Question 35

Question 35.

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 36

Which statement is FALSE?

Accepted Answer

The interval of increase is (-1, 2)

Answer

-4 is included in the domain, but 4 is not

Answer

The interval of decrease is (-4, 0)

Answer

The interval of increase is (0, 2)

Question 37

Where are the discontinuities of this function, if any exist?

Accepted Answer

at x = -3 and x = 1

Answer

at x = -3

Answer

at x = 1

Answer

there aren't any

Question 38

Identify the domain and range of the piecewise function.

Accepted Answer

Domain: $$x<-1\ or\ x>1$$

Range: $$y>2$$

Answer

Domain: $$x\in R$$

Range: $$y\in R$$

Answer

Domain: $$-1

Range: $$y>2$$

Answer

Domain: $$x<-1\ or\ x>1$$

Range: $$y>2\ or\ y=3$$

Question 39

Identify the interval behavior of the piecewise function.

Accepted Answer

Increasing: $$x>1$$

Decreasing: none

Constant: $$x<-1$$

Answer

Increasing: $$x>2$$

Decreasing: none

Constant: $$x<3$$

Answer

Increasing: none

Decreasing: $$x>2$$

Constant: $$x<3$$

Answer

Increasing: none

Decreasing: $$x>1$$

Constant: $$x<-1$$

Question 40

Identify the correct domain and range of the piecewise function.

Accepted Answer

Domain: $$x\in R$$

Range: $$y\in R$$

Answer

Domain: $$x<2\ or\ x\ge2$$

Range: $$y\in R$$

Answer

Domain: $$x\in R$$

Range: $$y<4\ or\ y\ge1$$

Answer

Domain: $$x<2\ or\ x>2$$

Range: $$y\in R$$

Question 41

Identify the interval behavior of the piecewise function.

Accepted Answer

Increasing: $$x<0$$

Decreasing: none

Constant: $$x>0$$

Answer

Increasing: $$-2\le x\le0$$

Decreasing: $$x\le-2$$

Constant: $$x\ge0$$

Answer

Increasing: $$-2

Decreasing: $$x<-2$$

Constant: $$x>0$$

Answer

Increasing: $$x<4$$

Decreasing: none

Constant: $$x>4$$

Question 42

Identify the domain and range of the piecewise function.

Accepted Answer

Domain: $$x\in R$$

Range: $$y\le4$$

Answer

Domain: $$x\in R$$

Range: $$y\in R$$

Answer

Domain: $$x\le4$$

Range: $$y\in R$$

Answer

Domain: $$x\in R$$

Range: $$y<4$$

Question 43

Describe the transformations: $$f\left(x\right)=-\left(x-2\right)^2+4$$

Accepted Answer

Translation: right 2, up 4

Reflection: over the x-axis

Dilation: none

Answer

Translation: left 2, up 4

Reflection: none

Dilation: wider

Answer

Translation: left 2, down 4

Reflection: over the x-axis

Dilation: none

Answer

Translation: right 2, up 4

Reflection: over the x-axis

Dilation: narrower

Question 44

Describe the transformations: $$f\left(x\right)=5\left(x+6\right)^2-1$$

Accepted Answer

Translation: left 6, down 1

Reflection: none

Dilation: narrower

Answer

Translation: up 5

Reflection: none

Dilation: wider

Answer

Translation: right 6, down 1

Reflection: over the x-axis

Dilation: narrower

Answer

Translation: left 6, up 1

Reflection: over the x-axis

Dilation: wider

Question 45

What is the domain?

Accepted Answer

$$x\in R$$

Answer

$$y\le6$$

Answer

$$x\le6$$

Answer

$$y\in R$$

Question 46

What is the range?

Accepted Answer

$$-4\le y\le5$$

Answer

$$-3<y\le3$$

Answer

$$-4<y\le5$$

Answer

$$-4<y<5$$

Question 47

Determine the equation for the red graph.

Accepted Answer

g(x) = (x - 1)³

Answer

g(x) = x³+ 1

Answer

g(x) = x³- 1

Answer

g(x) = (x + 1)³

Question 48

What is the domain?

Accepted Answer

$$-3<x\le3$$

Answer

$$-3<y\le3$$

Answer

$$-4\le y\le5$$

Answer

$$-4\le x\le5$$

Question 49

A function forms a straight line when graphed

Accepted Answer

SOMETIMES TRUE

Answer

ALWAYS TRUE

Answer

NEVER TRUE

Question 50

Use the graph shown to determine if the function is continuous at $$x=5$$ . If the function is not continuous, state the type of discontinuity the function has at that point.

Accepted Answer

The function has a jump discontinuity at $$x=5$$ .

Answer

The function is continuous at $$x=5$$ .

Answer

The function has a removable discontinuity (hole) at $$x=5$$ .

Answer

The function has a non-removable (infinite) discontinuity at $$x=5$$ .

Question 51

Use the graph shown to determine if the function is continuous at $$x=18$$ . If the function is not continuous, state the type of discontinuity the function has at that point.

Accepted Answer

The function has a removable discontinuity (hole) at $$x=18$$ .

Answer

The function is continuous at $$x=18$$ .

Answer

The function has a jump discontinuity at $$x=18$$ .

Answer

The function has a non-removable (infinite) discontinuity at $$x=18$$ .

Major Assessment #1: Functions Overview

82 questions

Given the function f(x) = x², which transformation would result in the graph of f(x) being shifted 3 units to the right?

Match the parent function with its graph's description

Match the parent function with its range

What is the effect of the transformation f(x) = -2 * g(x) on the graph of the function g(x)?

If h(x) = 1/4 * f(x), how is the graph of h(x) related to the graph of f(x)?

The function f(x) = (x - 2)² + 5 is a transformation of the parent function g(x) = x².
Describe the transformation.

What is the effect of the transformation f(x) = g(x + 4) - 1 on the graph of the function g(x)?

If the graph of f(x) = |x| is reflected over the x-axis, what is the new equation?

Given the function f(x) = x³, which transformation would result in the graph of f(x) being reflected over the y-axis?

What is the result of the transformation f(x) = 3 * g(x - 2) on the graph of the function g(x)?

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Major Assessment #1: Functions Overview

82 questions

Given the function f(x) = x2, which transformation would result in the graph of f(x) being shifted 3 units to the right?

Match the parent function with its graph's description

Match the parent function with its range

What is the effect of the transformation f(x) = -2 * g(x) on the graph of the function g(x)?

If h(x) = 1/4 * f(x), how is the graph of h(x) related to the graph of f(x)?

The function f(x) = (x - 2)2 + 5 is a transformation of the parent function g(x) = x2. Describe the transformation.

What is the effect of the transformation f(x) = g(x + 4) - 1 on the graph of the function g(x)?

If the graph of f(x) = |x| is reflected over the x-axis, what is the new equation?

Given the function f(x) = x3, which transformation would result in the graph of f(x) being reflected over the y-axis?

What is the result of the transformation f(x) = 3 * g(x - 2) on the graph of the function g(x)?

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Given the function f(x) = x², which transformation would result in the graph of f(x) being shifted 3 units to the right?

The function f(x) = (x - 2)² + 5 is a transformation of the parent function g(x) = x².
Describe the transformation.

Given the function f(x) = x³, which transformation would result in the graph of f(x) being reflected over the y-axis?