Free Printable Algebra 1: Topic 10 (Working with Functions)

1.

What type of function is this? $f\left(x\right)=\sqrt{x-1}-3$

a)

square root

b)

square

c)

absolute value

d)

quadratic

2.

Does the function $f\left(x\right)=2^x$ ever cross the x axis?

a)

No

b)

Yes

c)

Maybe

3.

What type of function is shown?

a)

square

b)

square root

c)

absolute value

d)

exponential

4.

What type of function is this?

a)

Exponential

b)

Square root

c)

Absolute Value

d)

Quadratic

5.

Which type of function is this?

a)

Square root

b)

Linear

c)

Absolute Value

d)

Quadratic

6.

What are the transformations of this functions compared to the parent function?

a)

Shifted down 2

b)

Shifted up 2

c)

Shifted left 2

d)

Shifted right 2

7.

What are the transformations of this functions compared to the parent function?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

c)

Reflected over the x-axis, vertical stretch by 2, and shifted left 5

d)

Shifted right 5, shifted down 2

8.

Which of these equations shifts a radical equation right 5 times and down once?

a)

y = √(x - 5) - 1

b)

y = √(x + 5) - 1

c)

y = √(x - 5) + 1

d)

y = √(x + 5) + 1

9.

Which of these equations shifts a radical equation left 3 times?

a)

y = √(x) + 3

b)

y = √(x) - 3

c)

y = √(x + 3)

d)

y = √(x - 3)

10.

Which of the following is the function shown in the graph?

a)

b)

c)

d)

11.

Let f(x)=√(x) and g(x)= -3√(x-2)+1. Describe g(x) in terms of f(x):

a)

reflects over x axis, vertical stretch by 3, right 2, up 1

b)

reflects over y axis, vertical compression by -3, left 2, up 1

c)

reflects over x axis, vertical stretch by -3, left 2, up 1

d)

reflects over y axis, vertical compression by 1/3, right 2, up 1

12.

Describe the transformation.

a)

Down 1

b)

Reflect over y-axis

c)

Up 1

d)

Reflect over x-axis

13.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

14.

What is the domain of the function in this graph?

a)

(-infinity, 3]

b)

[3, inifinity)

c)

(-infinity, 0]

d)

[0, infinity)

15.

What is the DOMAIN of the function?

a)

[-3, infinity)

b)

[0, infinity)

c)

[3, inifinity)

d)

(-infinity, 0}

16.

a)

$y=-\sqrt{x+1}$

b)

$y=\sqrt{x+1}$

c)

$y=-\sqrt{x}-1$

d)

$y=\sqrt{x}+1$

17.

What function best describes this graph?

a)

$y=-\sqrt{x+4}-2$

b)

$y=\sqrt{x-4}-2$

c)

$y=-\sqrt{x-4}-2$

d)

$y=\sqrt{x+4}+2$

18.

What is the X-INTERCEPT of this square root function?

a)

(0,0)

b)

(9,0)

c)

(0,-3)

d)

(1,1)

19.

What is the y-intercept of the graph?

a)

(-1,0)

b)

(0,-1)

c)

(0,3)

d)

(3,0)

20.

What is the Domain of ALL Cube Root Functions?

a)

(−∞,∞)

b)

[0,∞)

c)

(−∞,0]

d)

All Cube Root Functions are different.

21.

What is the Range of ALL Cube Root Functions?

a)

(−∞,∞)

b)

[0,∞)

c)

(−∞,0]

d)

All Cube Root Functions are different.

22.

Identify the Transformations.

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4

23.

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

24.

What kind of function is represented by the graph?

a)

Cube Root Function

b)

Cubic Function

c)

Polynomial Function

d)

Square Root Function

25.

Match the equation with the graph

a)

$y=\sqrt[3]{x-3}+5$

b)

$y=\sqrt[3]{x-3}-5$

c)

$y=\sqrt[3]{x+3}+5$

d)

$y=\sqrt[3]{x+3}-5$

26.

Which function matches the graph?

a)

A

f(x) = − ∛(x + 3) − 1

b)

B

f(x) = − ∛(x - 3) − 1

c)

C

f(x) = ∛(x + 3) − 1

d)

D

f(x) = ∛(x - 1) + 3

27.

Match the equation with the graph

a)

$y=\sqrt[3]{x-3}$

b)

$y=\sqrt[3]{x+3}$

c)

$y=\sqrt[3]{x}+3$

d)

$y=\sqrt[3]{x}-3$

28.

What is the x-intercept of the function?

a)

(32,0)

b)

(5,0)

c)

(27,0)

d)

(22,0)

29.

Find the cube root.

a)

9

b)

3

c)

-9

d)

-3

30.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

31.

Which statement is true about this graph?

a)

This function is always constant

b)

This function is always increasing

c)

This function is never increasing

d)

This function is both increasing and decreasing

32.

What is the domain of the graph?

a)

[1,∞)

b)

(-∞,1]

c)

(-∞,∞)

d)

[-∞,∞]

33.

What is the range of the graph?

a)

[1, ∞)

b)

(1, ∞)

c)

(-∞, ∞)

d)

none of these

34.

What is the interval of increase of this function?

a)

(1, ∞)

b)

None

c)

(2, ∞)

d)

(-∞, ∞)

35.

What is the range of this function?

a)

(1, ∞)

b)

[2, 4]

c)

[0, ∞)

d)

[2, ∞)

36.

What is the domain of this function?

a)

(0, ∞)

b)

[1, ∞)

c)

[1, 5]

d)

[2, ∞)

37.

Is the highlighted section of this graph increasing, decreasing or no change?

a)

increasing

b)

decreasing

c)

no change (stopped)

38.

Is the highlighted section of the graph increasing, decreasing, or no change?

a)

increasing

b)

decreasing

c)

no change (stopped)

39.

Is the highlighted section of the graph increasing, decreasing, or no change?

a)

increasing

b)

decreasing

c)

no change (stopped)

40.

What is the domain of the graph?

a)

from x = 1 to x = 4

b)

from x = 2 to x = 6

c)

from y = 1 to y = 4

d)

from y = 2 to y = 6

41.

What is the range of the graph?

a)

from x = 1 to x = 4

b)

from x = 2 to x = 6

c)

from y = 1 to y = 4

d)

from y = 2 to y = 6

42.

Is the shaded area Increasing, Decreasing, or Constant?

a)

Decreasing Interval

b)

Increasing Interval

c)

Constant Interval

d)

Positive Interval

e)

Negative Interval

43.

Consider: f(x) = 5x + 4

evaluate f(2)

a)

f(2) = 29

b)

f(2) = 11

c)

f(2) = 14

d)

f(2) = 56

44.

if f(1) = 5 and g(1) = 3,

Evaluate f(1) + g(1)

a)

2

b)

8

c)

10

d)

15

45.

Consider: f(x) = x² and g(x) = x+3

evaluate f(3) + g(3)

a)

6

b)

12

c)

15

d)

65

46.

What change does a Translation Cause?

a)

a shift up, down, left, or right

b)

a reflection

c)

a compression

d)

a stretch

47.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

48.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

49.

What are the transformations of this functions compared to the parent function?

a)

Shifted down 2

b)

Shifted up 2

c)

Shifted left 2

d)

Shifted right 2

50.

Describe the transformations of the graph y = (x - 3)³ -2

a)

Right 3, Down 2

b)

Left 3, Up 2

c)

Right 3, Up 2

d)

Left 3, Down 2

51.

Describe the transformations.

a)

Translate Right 2, Down 4

b)

Translate Left 2, Down 4

c)

Translate Left 2, Up 4

d)

Translate Right 2, Up 4

52.

f(n)=n²+4n
g(n)=-n-5
Find f(n)+g(n)

a)

n²+3n-5

b)

-n³+2n-7

c)

n³+3n-3n

d)

n²-3n-5

53.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

54.

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

55.

f(x) = 6x² + 3x + 2 and g(x) = x - 7

Find f(x) * g(x)

a)

6x³ - 39x² - 19x + 14

b)

6x³ - 39x² - 21x - 14

c)

6x³ - 39x² - 19x - 14

d)

6x³ - 45x² - 19x + 14

56.

$m(x)=x^2+3x-7$

g(x)=3x^2+5+2x

Find: g(x) - m(x)

a)

$4x^2+5x-2$

b)

$2x^2+x-12$

c)

$2x^2-x+12$

d)

$2x^2+x-2$

57.

$g(x)=3x^2+5+2x$ $p(x)=5x-1$
Find g(x) + p(x)

a)

$3x^2+7x-4$

b)

$3x^2+3x+4$

c)

$3x^2+7x+4$

d)

$3x^2+7x-5$

58.

$r(x)=-4x+9$
Find r(4)

(a)

59.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

60.

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

a)

True

b)

False

61.

Was the inverse function found correctly?

a)

no,

b)

yes

62.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

63.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

64.

a)

Inverse Functions

b)

Not Inverse Functions

65.

What does an inverse function do?

a)

Nothing

b)

Makes it bigger

c)

Does the opposite of the original function

Algebra 1: Topic 10 (Working with Functions)

Total questions: 65

Worksheet time: 1hrs 22mins

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