Free Printable Functions- Unit 1

1.

What is the domain of the graph?

a)

$-\infty<x<2$

b)

$-\infty<y\le1$

c)

$-\infty<x<\ \infty$

d)

$1<x<3$

2.

Match the graph with the correct equation.

a)

b)

c)

d)

3.

Describe the transformation from the parent absolute value function:

$y=-\left|x+4\right|-3$

* Select THREE answers *

a)

Reflection over the x-axis

b)

Translation 4 units left

c)

Translation 4 units up

d)

Translation 3 units left

e)

Translation 3 units down

4.

Describe the transformation(s) in the following function.

$f\left(x\right)=\frac{4}{5}\left|x+5\right|+2$

a)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

b)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

c)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

d)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift up 2 units

e)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

5.

Describe the parent graph transformation

a)

Vertical stretch by 1/2, left 1, down 3

b)

Vertical stretch by 1/2, right 1, down 3

c)

Vertical Shrink by 1/2, left 1, down 3

d)

Vertical Shrink by 1/2, right 1, down 3

6.

What is the Range?

a)

$\left(-\infty,\infty\right)$

b)

(6, $,\infty$ )

c)

( $-\infty$ ,6]

d)

( $-\infty,$ 2]

7.

What is the range of the function?

a)

[2, $\infty$ )

b)

[-1, $\infty$ )

c)

[-2,2]

d)

( $-\infty,\infty$ )

8.

What is the domain of the relation graphed?

a)

( $-\infty,\infty$ )

b)

( $-\infty,$ -4]

c)

[-4, $\infty$ ]

d)

( $-\infty$ 0 ]

9.

Evaluate for f(1)

a)

0

b)

-3

c)

3

d)

2

10.

For this graph complete the following end behavior: As x --> -∞, f(x) --> _(A)_

As x --> +∞, f(x) --> _(B)_

a)

A= -∞

B= -∞

b)

A= +∞

B= -∞

c)

A= -∞

B= +∞

d)

A= +∞

B= +∞

11.

What are the zeros of the function?

a)

4, 1

b)

-3, -1, 2, 5

c)

-3, -1, 30, 2, 5

d)

3, 1, -2, -5

12.

The blue dot on this graph represents a(n)...

a)

Absolute Maximum

b)

Absolute Minimum

c)

Local Maximum

d)

Local Minimum

13.

Which equation describes the transformation of shifting f(x)=x² two units right?

a)

x² + 2

b)

x² - 2

c)

(x + 2)²

d)

(x - 2)²

14.

What are the following transformations?
- f(x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

15.

What is the equation of this graph?

a)

f(x) = (x + 2)² - 3

b)

f(x) = (x - 2)² - 3

c)

f(x) = |x + 2| - 3

d)

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

16.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

a)

-f(x)

b)

f(-x)

c)

f^-1(x)

d)

f(2x)

17.

What is the domain interval for the green piece of this function?

a)

-2 < x ≤ 1

b)

-1 < x ≤ 0.5

c)

x > -2

d)

x ≤ 1

18.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

19.

What is f(6)?

a)

20

b)

33

c)

3

d)

3, -3

20.

a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

21.

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$

a)

No vertical asymptotes.

b)

One vertical asymptote: x = 4

c)

Two vertical asymptotes: x = -3 and x = -7

d)

Three vertical asymptotes: x = -3, x = 4, and x = -7

22.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

23.

What is the oblique asymptote for the function?

a)

y = 12

b)

y = x - 5

c)

y = x-5 + 12/(x+2)

d)

y = 12/(x+2)

24.

Identify the Oblique Asymptote for this function.

a)

y = 5x - 7

b)

y = 5x + 13

c)

y = 5x + 3

d)

y = 5x + 7

25.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

26.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

27.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

28.

Factor completely.
3x²- 9x -120

a)

3(x - 8)(x + 5)

b)

3(x + 8)(x - 5)

c)

(3x + 8)(x - 5)

d)

(3x - 8)(x + 5)

29.

What is F(-8)?

a)

2

b)

-4

c)

-2

d)

0

30.

$k\left(n\right)=3n^2-1-2n$ Find $k\left(n+4\right)$

a)

$3n^4-1\ -2n$

b)

$-1-n+\frac{3}{4}n^2$

c)

$3n^2+22n+39$

d)

$\frac{1}{3}n^2-\frac{2}{3}n-1$

31.

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the height of the cliff?

a)

1.094 ft

b)

174.141 ft

c)

155 ft

d)

4.393 ft

e)

None of the above

32.

Factor:
2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

33.

Factor:

60x²y - 3xy

a)

3x²y (20x -1)

b)

3xy (20x +1)

c)

3xy (20x - 1)

d)

-3xy (20x - 1)

34.

Identify the equation of the graph.

a)

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

b)

$y=\sqrt{x+1}$

c)

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

d)

$y=\sqrt{x}+1$

35.

Describe the translation of the function $y=2+3\ \sqrt[]{x+1}$ .

a)

left 1 unit, down 2 units, vertical stretch by 3

b)

left 1 unit, up 2 units, vertical stretch by 3

c)

left 1 unit, up 2 units, vertical stretch by 1/3

d)

right 1 unit, up 2 units

Functions- Unit 1

Total questions: 35

Worksheet time: 59mins

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