Free Printable Major Assessment #1: Functions Overview

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Major Assessment #1: Functions Overview

Total questions: 82

Worksheet time: 9hrs 47mins

Name

Class

Date

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

f(x) = (x - 3)^2

f(x) = (x + 3)^2

f(x) = x^2 + 3

f(x) = x^2 - 3

Match the parent function with its graph's description

A v-shaped graph centered at the origin

y = |x|

A parabola opening upwards centered at the origin

y = x²

A graph that starts at the origin and increases slowly

$y=\sqrt[]{x}$

A straight line passing through the origin

y = x

Match the parent function with its range

Nonlinear with an endpoint at the origin

$y=\sqrt{x}$

Nonlinear with two ends pointing in opposite directions

$y=x^3$

Nonlinear with a minimum point

$y=x^2$

Nonlinear with a sharp turn at the origin

$y=\left|x\right|$

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

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

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

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

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

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

It is horizontally stretched by a factor of 4

It is horizontally compressed by a factor of 4

It is vertically stretched by a factor of 4

It is vertically compressed by a factor of 4

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

Describe the transformation.

Shifted 2 units to the right and 5 units up

Shifted 2 units to the left and 5 units up

Shifted 2 units to the right and 5 units down

Shifted 2 units to the left and 5 units down

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

Shifted 4 units to the left and 1 unit up

Shifted 4 units to the right and 1 unit up

Shifted 4 units to the left and 1 unit down

Shifted 4 units to the right and 1 unit down

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

f(x) = -|x|

f(x) = |x|

f(x) = |x| + 1

f(x) = -|x| - 1

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

f(x) = -x^3

f(x) = (x + 3)^3

f(x) = (-x)^3

f(x) = x^3 + 3

10.

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

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

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

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

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

11.

If the function f(x) = √x is horizontally compressed by a factor of 1/2, what is the new function?

f(x) = √(2x)

f(x) = √(x/2)

f(x) = 2√x

f(x) = (1/2)√x

12.

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

Reflected over the x-axis

Reflected over the y-axis

Reflected over both the x-axis and y-axis

No transformation has occurred

13.

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?

14.

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)?

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

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

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

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

15.

Which of the following is the parent function for $y=\left(\frac{2}{3}x\right)^2$ ?

Fill in the blank.
f(x) = ____

16.

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]

17.

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

18.

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

19.

Graph y = -(x +4)² - 3

20.

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

TRUE

FALSE

21.

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

TRUE

FALSE

22.

A linear equation is an example of a parent function.

TRUE

FALSE

23.

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]

10 feet

18 feet

16 feet

20 feet

24.

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

TRUE

FALSE

25.

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

TRUE

FALSE

26.

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

$15

$17

$19

$21

27.

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.

$12

$14

$10

28.

The function f(x) = 60x computes the number of minutes in x hours. The function g(x) = 24x computes the number of hours in x days. What is (f ∘ g)(x) and what does it compute?

(f ∘ g)(x) = 84x;

It computes the number of minutes plus the number of days in x days.

(f ∘ g)(x) = 1440x;

It computes the number of days in x minutes.

(f ∘ g)(x) = 1440x²;

It computes the number of minutes in x days.

(f ∘ g)(x) = 1440x;

It computes the number of minutes in x days

29.

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

-1

-2

30.

Fill in the blank.
If f(x) = 5x - 3

and g(x) = x - 4 ,

then $g\left(f\left(-3\right)\right)=_{ }$ ___

31.

Fill in the blank.

If f(x) = 5x - 2 and

g(x) = x - 5 ,
then $f\left(g\left(2\right)\right)=$ ___

32.

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

Always True

Sometimes True

Never True

33.

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

Always True

Sometimes True

Never True

34.

A function graph has a vertex point.

Always True

Sometimes True

Never True

35.

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

Always True

Sometimes True

Never True

36.

Domain is: (a)

Choose from the below words

all x values, from left to right.

all x values from bottom to top.

all y values, from bottom to top.

all y values from left to right.

37.

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

largest f (x);

smallest m (x)

largest m (x); smallest g (x)

largest g (x);

smallest m (x)

largest g (x);

smallest f (x)

38.

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?

6 ft/mph

60 ft/mph

10 ft/mph

120 ft/mph

39.

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]

positive

negative

constant

[means fixed]

1 on interval [1,4]

-1 on interval [-2,0]

40.

Which of the following statements is TRUE regarding functions

f (x) and g(x) shown?

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

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

Both functions have the same rate of change.

There is insufficient information to determine the rate of change.

41.

Which graph possesses the following features?
• decreasing on (2,3)
• increasing on (3,∞)
• relative minimum at (3,-4)
• positive on (-1,2)

42.

Which of the following functions has the characteristics:
• domain all Reals
• increasing (-∞, ∞)
• positive (0, ∞)
• as x → ∞, y → ∞
• as x → -∞, y → 0

43.

Which choice describes the end behavior for the graph shown?

44.

Organize these options into the right categories

Categorize the following

DISCRETE

CONTINUOUS

NEITHER

45.

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?

46.

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

Which of the following equations represents this graph?

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

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

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

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

47.

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

Which choice is an end behavior for this function?

As x → -∞, f (x) → -∞.

As x → -∞, f (x) → ∞.

As x → -5, f (x) → ∞.

As x → -5, f (x) → -∞.

48.

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?

quadratic

linear

exponential

absolute value

49.

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 was the maximum number of albums sold in one week?

50.

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?

1,000 albums per week

2,000 albums per week

3,000 albums per week

4,000 albums per week

51.

The minimum point on the graph of the function y = f (x) is (-2,-4).

What is the minimum point on the graph of the function y = f (x) + 7?

(a)

52.

Kiara tutors students to earn spending money. She charges an hourly rate to tutor on weekdays after school and a higher hourly rate to tutor on weekends. The following graph represents Kiara’s earnings in one week beginning on Monday.

Which of the following statements are true? Select all that apply

Kiara tutors eight hours on weekdays after school.

Kiara charges $20 per hour to tutor on the weekends.

Kiara tutors 15 hours over the weekend.

Kiara earned $80 tutoring on weekdays after school.

Kiara earned $185 tutoring on the weekend

53.

In a parent function, the highest or lowest point in the graph is referred to as the vertex. (a)

Choose from the below words

TRUE

FALSE

54.

The concept of domain and range does not apply to the graph of a parent function. (a)

Choose from the below words

FALSE

TRUE

55.

The parent function of a linear function is represented by f(x) = x². (a)

Choose from the below words

FALSE

TRUE

56.

It is possible for a piecewise function to be both linear and quadratic in different intervals of its domain. (a)

Choose from the below words

TRUE

FALSE

57.

A piecewise function, by definition, must be continuous. (a)

Choose from the below words

FALSE

TRUE

58.

The graph of a piecewise function usually has breaks, jumps, or holes. (a)

Choose from the below words

TRUE

FALSE

59.

In the notation of a function, f(x) = x², the f(x) is called the input. (a)

Choose from the below words

FALSE

TRUE

60.

A piecewise function is a type of function that can only have one rule for the entire domain. (a)

Choose from the below words

FALSE

TRUE

61.

62.

Which statement is FALSE?

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

The interval of decrease is (-4, 0)

The interval of increase is (-1, 2)

The interval of increase is (0, 2)

63.

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

at x = -3 and x = 1

at x = -3

at x = 1

there aren't any

64.

Identify the domain and range of the piecewise function.

Domain: $x\in R$

Range: $y\in R$

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

Range: $y>2$

Domain: $-1<x<1$

Range: $y>2$

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

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

65.

Identify the interval behavior of the piecewise function.

Increasing: $x>2$

Decreasing: none

Constant: $x<3$

Increasing: $x>1$

Decreasing: none

Constant: $x<-1$

Increasing: none

Decreasing: $x>2$

Constant: $x<3$

Increasing: none

Decreasing: $x>1$

Constant: $x<-1$

66.

Identify the correct domain and range of the piecewise function.

Domain: $x\in R$

Range: $y\in R$

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

Range: $y\in R$

Domain: $x\in R$

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

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

Range: $y\in R$

67.

Identify the interval behavior of the piecewise function.

Increasing: $-2\le x\le0$

Decreasing: $x\le-2$

Constant: $x\ge0$

Increasing: $-2<x<0$

Decreasing: $x<-2$

Constant: $x>0$

Increasing: $x<0$

Decreasing: none

Constant: $x>0$

Increasing: $x<4$

Decreasing: none

Constant: $x>4$

68.

Identify the domain and range of the piecewise function.

Domain: $x\in R$

Range: $y\in R$

Domain: $x\le4$

Range: $y\in R$

Domain: $x\in R$

Range: $y<4$

Domain: $x\in R$

Range: $y\le4$

69.

The graph of an absolute value function has two y −intercepts.

(a)

Choose from the below words

always true

sometimes true

never true

70.

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

Translation: left 2, up 4

Reflection: none

Dilation: wider

Translation: left 2, down 4

Reflection: over the x-axis

Dilation: none

Translation: right 2, up 4

Reflection: over the x-axis

Dilation: none

Translation: right 2, up 4

Reflection: over the x-axis

Dilation: narrower

71.

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

Translation: up 5

Reflection: none

Dilation: wider

Translation: right 6, down 1

Reflection: over the x-axis

Dilation: narrower

Translation: left 6, down 1

Reflection: none

Dilation: narrower

Translation: left 6, up 1

Reflection: over the x-axis

Dilation: wider

72.

If an absolute value function (i.e. y = a │x – h│ + k ) opens up, which is true?

a is positive

a is the number zero

a is negative

a is 1

73.

What is the domain?

$x\in R$

$y\le6$

$x\le6$

$y\in R$

74.

What is the range?

$-3<y\le3$

$-4\le y\le5$

$-4<y\le5$

$-4<y<5$

75.

Determine the equation for the red graph.

g(x) = x³+ 1

g(x) = (x - 1)³

g(x) = x³- 1

g(x) = (x + 1)³

76.

What is the domain?

$-3<y\le3$

$-4\le y\le5$

$-4\le x\le5$

$-3<x\le3$

77.

A function forms a straight line when graphed

ALWAYS TRUE

SOMETIMES TRUE

NEVER TRUE

78.

Identify the coordinates of the point (3 , -2), translated 5 units left and 6 units up.

(a)

79.

Range is (a)

Choose from the below words

all x values, from left to right.

all y values, from left to right.

all x values, from bottom to top.

all y values, from bottom to top.

80.

In linear functions, as x → ∞, y → −∞.

(a)

Choose from the below words

always true

never true

sometimes true

81.

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.

The function is continuous at $x=5$ .

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

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

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

82.

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.

The function is continuous at $x=18$ .

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

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

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

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Major Assessment #1: Functions Overview

Total questions: 82

Worksheet time: 9hrs 47mins

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