Free Printable LHS Functions 1st Unit - Homework For all Targets

1.

1) Give the domain for the following graph. Write the domain in words, using symbols, set notation and interval notation.

Words: __________

Set Notation: __________

Interval Notation: __________

a)

Words: All real numbers

Set Notation: {x | x ∈ ℝ}

Interval Notation: (-∞, ∞)

b)

Words: All non-negative numbers

Set Notation: {x | x ≥ 0}

Interval Notation: [0, ∞)

c)

Words: All negative numbers

Set Notation: {x | x < 0}

Interval Notation: (-∞, 0)

d)

Words: All integers

Set Notation: {x | x ∈ ℤ}

Interval Notation: (-∞, ∞)

2.

2) Give the domain for the following equations. You may use symbols.

a) f(x) = (4x - 3) / (2x + 1) Domain:___________________

b) g(x) = √(2x + 9) Domain:___________________

c) h(x) = 4 / ((x - 8)(x + 3)) Domain:___________________

a)

a) f(x): ℝ x ≠ -1/2;

g(x): x ≥ -9/2;

h(x): ℝ x ≠ 8, x ≠ -3

b)

b) f(x): ℝ x ≠ 1/2;

g(x): x ≥ -9/2;

h(x): ℝ x ≠ 8, x ≠ 3

c)

c) f(x): ℝ x ≠ -1/2;

g(x): x ≥ 9/2;

h(x): ℝ x ≠ 8, x ≠ -3

d)

d) f(x) ℝ: x ≠ -1/2;

g(x): x ≥ -9/2;

h(x): ℝ x ≠ -8, x ≠ 3

3.

3) Give the domain and range for the following graph. Use each kind of notation as indicated.

Domain: Interval Notation __________________________,

Range: Inequality Notation __________________________.

a)

Domain: All real numbers, Range: All real numbers

b)

Domain: [ -∞, 1 )

Range: y ≥ 0

c)

Domain: ( -∞ , ∞ )

Range: -∞ < y < ∞

d)

Domain: ( -∞, 1 ]

Range: y ≥ 0

4.

Domain and range for the graph

Domain: __________

Range:___________

a)

Domain: ( -4, 6 )

Range: [ -2, 3 ]

b)

Domain: (-4, -2, 0, 2, 4, 5, 6)

Range: (-2, 0, 1, 2, 3)

c)

Domain: [ -4, 6 ]

Range: [ -2, 3 ]

d)

Domain: A House

Range: A place you raise horses

5.

Use the graph to answer the question f(-4) = __________

a)

f(-4) = -2

b)

f(-4) = 2

c)

f(-4) = 0

d)

f(-4) = 1

6.

Use the graph to answer the question f(6) = __________

a)

f(6) = -2

b)

f(6) = 2

c)

f(6) = 0

d)

f(6) = 3

7.

Is f(3) positive or negative?

a)

Positive

b)

Negative

8.

Is f(-1) positive or negative?

a)

Positive

b)

Negative

9.

For what numbers is f(x) = 0?

Select ALL correct answers

a)

x = 0

b)

x = 2

c)

x = 4

d)

x = 6

10.

This graph is in three of the four quadrants. What quadrant does NOT have any of the graph "in it"?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

11.

Use the graph to answer the questions. i) Name the x-intercepts: __________ Name the y-intercepts: __________

a)

x-intercepts @

(5 3),

(4, 0),

(6, 0)

y-intercepts @ (0,0)

b)

x-intercepts @

(0, 0),

(4, 0),

(6, 0)

y-intercepts @ (2,-2)

c)

x-intercepts @

(0, 0),

(4, 0),

(6, 0)

y-intercepts @ (0,0)

d)

There are none

12.

For the following graph write "function" or "not a function".

a)

function

b)

not a function

13.

For the following graph write "function" or "not a function".

a)

function

b)

not a function

14.

For the following graph write "function" or "not a function".

a)

function

b)

not a function

15.

List the domain and range for $f\left(x\right)\ =\ x^2$ . Domain: ______ Range: ______

a)

Domain: All real numbers, Range: y ≥ 0

b)

Domain: x ≥ 0, Range: y ≥ 0

c)

Domain: All real numbers, Range: All real numbers

d)

Domain: x ≥ 0, Range: All real numbers

16.

List the domain $g(x) = 2^x$ . What is the domain of $g(x)$ ?

a)

All real numbers

b)

x > 0

c)

x < 0

d)

x ≥ 0

17.

What is the range of the function $g\left(x\right)=2^x$

a)

The set of all real numbers

b)

The set of all positive integers

c)

The set of all integers

d)

The set of all non-negative real numbers

18.

Parent function $f\left(x\right)=x^2$ .

Write the new equation if you translated the parent Up 3. __________. Remember to start with f(x) =

19.

Parent function $y = \frac{1}{x}$ .

Describe the transformation(s) of $y = \frac{1}{x+5}$

a)

The transformation of the parent function is a horizontal shift 5 units to the left.

b)

The transformation of the parent function is a vertical shift 5 units up.

c)

The transformation of the parent function is a horizontal shift 5 units to the right.

d)

The transformation of the parent function is a vertical shift 5 units down.

20.

Parent function $y = |x|$ .

If you transform the function Up 2 and left 5. Write the equation of the translated figure

a)

y = |x + 5| + 2

b)

y = |x - 5| - 2

c)

y = |x + 5| - 2

d)

y = |x - 5| + 2

21.

Parent function $y = \sqrt{x}$ . Describe the transformation(s) of $y = 5\sqrt{x}$

a)

$5\sqrt{x}$

b)

y = $\sqrt{5x}$

c)

y = $\frac{1}{5}\sqrt{x}$

d)

y = $\sqrt{x}$ + 5

22.

Parent function $w\left(x\right)=2^x$ .

Describe the transformation(s) if reflected over the x-axis only

a)

w(x) = 2^x + 3

b)

w(x) = -2^x + 3

c)

w(x) = -2^x

23.

Parent function $y = \log_2(x)$ . Describe the transformation(s) of $y = \log_2(x-7)$

a)

The transformation is a horizontal shift to the right by 7 units.

b)

The transformation is a vertical shift upwards by 7 units.

c)

The transformation is a horizontal shift to the left by 7 units.

d)

The transformation is a vertical shift downwards by 7 units.

24.

Parent function $y = |x|$ .

If you were to Vertically Compress the function by 1/4, which equation matches?

a)

y = $\frac{1}{4}|x|$

b)

y = 4|x|

c)

y = |x|+1/4

d)

y = |x/4|

25.

Parent function $y = \sqrt[3]{x}$ .

Describe the transformation(s) of $y = \sqrt[3]{x} + 1$

a)

The parent function is shifted down by 1 unit.

b)

The parent function is shifted up by 1 unit.

c)

The parent function is shifted left by 1 unit.

d)

The parent function is shifted right by 1 unit.

26.

Parent function $y = x$

what is the equation if you were to vertically stretch it by 6?

(a)

27.

Parent function $y = |x|$ . Which of the following statements is true about $y = \frac{1}{2}|x|$ ?

a)

y = $\frac{1}{2}|x|$ is a vertical compression of the parent function y = $|x|$ by a factor of 1/2.

b)

y = $\frac{1}{2}|x|$ is a vertical compression of the parent function y = $|x|$ by a factor of 2.

c)

y = $\frac{1}{2}|x|$ is a horizontal compression of the parent function y = $|x|$ by a factor of 1/2.

d)

y = $\frac{1}{2}|x|$ is a reflection of the parent function y = $|x|$ across the x-axis.

28.

Given the graph of $f(x)$ , use the same set of axes to graph $f(x) + 2$ . What transformation is applied to the graph of $f(x)$ ?

a)

Vertical shift up by 2 units

b)

Vertical shift down by 2 units

c)

Horizontal shift left by 2 units

d)

Horizontal shift right by 2 units

29.

What is the y-coordinate of the point where the graph intersects the y-axis?

a)

0

b)

1

c)

2

d)

3

30.

At which x-coordinate does the graph have a peak?

a)

x = -2

b)

x = 0

c)

x = 3

d)

x = 4

31.

What is the x-coordinate of the point where the graph touch the x-axis?

Also known as 'roots', 'x-intercepts', 'solutions'

Select ALL correct answers

a)

0

b)

-5

c)

2

d)

3

32.

Fill in the blanks. Parent function $y = \sqrt[3]{x}$ Up 3. What is the transformed function?

a)

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

b)

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

c)

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

d)

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

33.

What is the equation for transformed function for $y=\frac{1}{x}$ if you shifted right 3 and down 1

a)

y = $\frac{1}{x-1}$ +3

b)

y = $\frac{1}{x+3}$ - 1

c)

y = $\frac{1}{x-3}$ + 1

d)

y = $\frac{1}{x-3}$ - 1

34.

What is the transformation of the function for $y = \frac{1}{x} - 2$ ?

a)

Left 2

b)

Down 2

c)

Right 2

d)

Up 2

35.

Fill in the blanks. Parent function $y = \frac{1}{x}$ . What is the transformed function for $y = \frac{-2}{x}$ ?

a)

Vertical Stretch by 2

&

Reflected over y-axis

b)

Vertical Stretch by 2

&

Reflected over x-axis

c)

No change

d)

Vertical Compression by 2

&

Reflect over x-axis

36.

What is the transformed function for $y = \frac{1}{-2(x-2)}$ ?

a)

Vertical Compression by 2

&

Reflection over x-axis

&

Left 2

b)

Vertical Compression by 1/2

&

Reflection over x-axis

&

Right 2

37.

What is the transformed function for $y = \frac{1}{5x} + 3$ ?

Select ALL that apply!!!

a)

Vertical Stretch by 1/5

b)

Up 3

c)

Vertical Compression by 1/5

d)

Down 3

38.

Fill in the blanks. Parent function $y=|x-3|-5$ What is the transformed function? (a) (b)

Choose from the below words

down 3

up 5

left 3

right 3

down 5

39.

What is the transformed function for y = √x if you transform it by moving it up 1/2 and reflect it over the line y=0?

a)

y = $-\sqrt{x} + \frac{1}{2}$

b)

y = $\sqrt{x} - \frac{1}{2}$

c)

y = $-\sqrt{x}-\frac{1}{2}$

d)

y = $\sqrt{x} + \frac{1}{2}$

40.

What is the function equation of $y=\log_2x$ transformed by shifting it right 7

a)

Parent function $y = 2^x$

b)

Transformed function $y = \log_2(x)$

c)

Transformed function $y = \log_2(x+7)$

d)

Transformed function $y = \log_2(x-7)$

41.

Parent function f(x) = ³√x → f(x) = ³√x + 1 is transformed how?

a)

down 1

b)

left 1

c)

up 1

d)

Right 1

42.

Parent function f(x) = x → f(x) = 6x is a?

a)

Horizontal Stretch by factor 6

b)

Vertical Stretch by factor 6

43.

g(k) = 1/2 |k|, What is the parent function?

a)

f(k) = |k|

b)

g(k) = 1/2 |k|

c)

k(g) = 1/2 |g|

44.

Given that f(x) = -3x² + 2x - 5 and g(x) = 2x - 1, find f(g(x))

a)

-3(2x - 1)² + 2(2x - 1) - 5

b)

-3(2x - 1)² + 2x - 5

c)

-3x² + 2(2x - 1) - 5

d)

-3x² + 2x - 5

45.

Given that f(x) = -3x² + 2x - 5 and g(x) = 2x - 1, find g(f(x))

a)

-6x² + 4x - 7

b)

-6x² + 4x - 6

c)

-6x² + 4x - 11

d)

-6x² + 4x - 4

46.

Given that f(x) = -3x² + 2x - 5 and g(x) = 2x - 1, find f(g(-4))

a)

-61

b)

-275

c)

-266

d)

-95

47.

Given the graph of $f(x)$ , what transformation is applied to graph $f(x - 4)$ on the same set of axes?

a)

Shift 4 units to the right

b)

Shift 4 units to the left

c)

Shift 4 units up

d)

Shift 4 units down

48.

Given the graph of $f(x)$ , what transformation occurs to graph $f(x) + 5$ on the same set of axes?

a)

The graph shifts 5 units up.

b)

The graph shifts 5 units down.

c)

The graph shifts 5 units to the right.

d)

The graph shifts 5 units to the left.

49.

Given the graph of $f(x)$ , which of the following represents the graph of $-f(x)$ on the same set of axes?

a)

The graph is reflected over the x-axis.

b)

The graph is shifted up.

c)

The graph is shifted down.

d)

The graph is reflected over the y-axis.

50.

1) Give the domain for the following graph.

a)

Interval Notation:

(-∞, ∞)

b)

Interval Notation: (-5, 1)

c)

Interval Notation: (-∞, 0)

d)

Interval Notation: (-5, 1]

51.

1) Give the Range for the following graph.

a)

Interval Notation:

(-∞, ∞)

b)

Interval Notation: [-3, 1)

c)

Interval Notation: (-3, 1)

d)

Interval Notation: [-3, 1]

52.

Give the domain for the equation f(x) = 3x / (3x - 1). You may use symbols.

a)

All real numbers except x = 1/3

b)

All real numbers except x = 0

c)

All real numbers except x = -1/3

d)

All real numbers

53.

Give the domain for the equation g(x) = √(4x + 1). You may use symbols.

a)

ℝ x ≥ -1/4

b)

ℝ x > -1/4

c)

ℝ x ≤ -1/4

d)

ℝ x < -1/4

54.

Give the domain for the equation h(x) = 4x / (x(x - 2)(5x + 1)).

a)

All real numbers x ≠ 0, x ≠ 2, and x ≠ -1/5

b)

All real numbers except x = 0 and x = 2

c)

All real numbers x = 2 and x = -1/5 and x = 0

d)

All real numbers

55.

Give the domain and range of the graph

a)

Domain: All real numbers

Range: All real numbers

b)

Domain: x ≥ 0

Range: y ≥ 0

c)

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

d)

Domain: -∞ < x < ∞

Range: -∞ < y < 1

56.

4) What is the domain and range for the graph at right (use symbols)?

a)

Domain: (-∞, ∞), Range: (-∞, 10)

b)

Domain: [0, ∞), Range: [0, ∞)

c)

Domain: (-∞, 0], Range: (-∞, 0]

d)

Domain: (-∞, ∞), Range: (-∞, 10]

57.

Use the graph to answer the questions. $f(2) =$ (a)

58.

Use the graph to answer the questions. $f(11)=$ (a)

59.

Which phrase best describes Domain?

a)

The set of all x-values for which the graph is defined

b)

The set of all y-values for which the graph is defined

c)

The set of all points where the graph intersects the x-axis

d)

The set of all points where the graph intersects the y-axis

60.

Use the graph to answer the questions. What is the Range?

a)

2 to 13

b)

1 to 8

c)

2 to 10

d)

30 to 40

61.

For the following graph, determine if it is a function or not. 1)

a)

Function

b)

Not a function

62.

For the following graph write "function" or "not a function". 2)

a)

Function

b)

Not a function

63.

For the following graph write "function" or "not a function". 3)

a)

Function

b)

Not a function

64.

For the following graph write "function" or "not a function". 4)

a)

Function

b)

Not a function

65.

For the following graph, determine if it is a function or not. 5)

a)

Function

b)

Not a function

66.

For the following graph, determine if it is a function or not. 6)

a)

Function

b)

Not a function

67.

What is the domain of the function $f(x) = \frac{1}{x}$ ?

a)

All real numbers except 0

b)

All real numbers

c)

All positive numbers

d)

All negative numbers

68.

What is the domain of the function $g(x) = \sqrt{x}$ ?

a)

x ≥ 0

b)

x > 0

c)

x ≤ 0

d)

x < 0

69.

Name the function

a)

Linear

b)

Quadratic

c)

Logarithm

d)

Cubic

70.

Name the function

a)

Linear

b)

Cubic

c)

Exponential Decay

d)

Exponential Growth

71.

Name the function

a)

Ellipse

b)

Logarithmic

c)

Reciprocal

d)

Cube root

72.

Name the function

a)

Square Root

b)

Logarithm

c)

Cube Root

d)

Linear

73.

Name the function

a)

Linear

b)

Goofy

c)

Quadratic

d)

Absolute Value

74.

Graph the piecewise function

h(x) = 2 when $x\le1$ AND h(x) = x when $x>1$

The format of what follows shows weird on your end
$h(x) = \begin{cases} 2 & \text{if } x \leq 1 \ x & \text{if } x > 1 \end{cases}$ ?

75.

Name the function

a)

Linear

b)

Quadratic

c)

Square Root

d)

Absolute Value

e)

Reciprocal

76.

Match the following graphs to their equations below. GRAPH C:

a)

y = |x|

b)

y = x

c)

$y = 2^x$

d)

y = 1/x

e)

$y = x^3$

77.

Match the graph to the equation

a)

y = |x|

b)

y = x

c)

$y = 2^x$

d)

y = 1/x

e)

$y = x^3$

78.

Match the following graphs to their equations below.

a)

y = |x|

b)

y = x

c)

$y = 2^x$

d)

y = 1/x

e)

$y = x^3$

79.

Write the domain for the following function Using interval notation: $f(x) = \frac{2x}{3x-5}$ .

a)

All real #'s x ≠ 5

b)

All real #'s x ≠ 5/3

c)

All real #'s x ≠ - 5/3

80.

Write the domain for the following function: $g(x) = \sqrt{2x+3}$ .

a)

x ≥ -3/2

b)

x > -3/2

c)

x ≤ -3/2

d)

x < -3/2

81.

Write the domain for the following function using method of your choice: $j(x) = \frac{(x-8)}{(x+1)(x-3)}$ .

a)

All real #s

x ≠ 1

x ≠ -3

b)

All real #s

x ≠ -1

x ≠ -3

c)

All real #s

x ≠ -1

x ≠ 3

d)

All Real #s

x ≠ 8

x ≠ -1

x ≠ 3

82.

Write the domain for the following function using method of choice: $h(x) = \sqrt{4x-5}$ .

a)

x < 5/4

b)

x > 5/4

c)

x ≤ 5/4

d)

x ≥ 5/4

83.

Write the domain for the following function using method of choice: $k(x) = \frac{4x+1}{x^2-16}$ .

a)

All real #s

x ≠ 16

b)

All real #s

x ≠ 4

x ≠ -4

c)

All real #s

x ≠ 4

d)

All real #s

x ≠ 1

x ≠ -1/4

84.

Graph the piecewise function $f(x) = \begin{cases} x^2, & \text{for } x \leq 0 \ 5, & \text{for } 0 < x < 2 \ x/2, & \text{for } x \geq 2 \end{cases}$ is the graph correct?

a)

True

b)

False

85.

Graph

f(x)= x² when $x<2$ ;

f(x)=6 when x=2;

f(x)= -x+10 when $2<x\le6$

86.

Find the average rate of change for the function $h(x) = -2x^2 + 5x$ from $x = -3$ to $x = 2$ .

a)

5

b)

-7

c)

7

d)

-5

87.

Which of the following best describes the behavior of a step function?

a)

It is continuous and smooth.

b)

It has sudden jumps at certain points.

c)

It is always increasing.

d)

It is always decreasing.

88.

What is the value of y when x = 0?

a)

-3

b)

4

c)

2

d)

0

89.

How much would postage cost for a letter that weighs 2.1 ounces?

a)

41 cents

b)

39 cents

c)

45 cents

d)

43 cents

90.

Morgan can start wrestling at age 5 In Division 1. She remains in that division until his next odd birthday when he is required to move up to the next Division level. Which graph correctly represents this information

a)