Free Printable 10-3 Analyzing Functions

1.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

2.

$y\ =\ \frac{4}{5}x-9$
$y\ =\ 5x\ +1$
These lines are _________________.

a)

Parallel

b)

Perpendicular

c)

Neither

3.

Select all the statements that are TRUE.

a)

Parallel lines have the same slope.

b)

Perpendicular lines have slopes that are opposite reciprocals.

c)

A horizontal line has a slope equal to zero.

d)

A vertical line has a slope that is undefined.

e)

Slope-intercept form is $y=mx+b$

4.

Which equation below is neither perpendicular nor parallel to $f\left(x\right)$ ?

$f\left(x\right)=\ \frac{1}{2}x-3$

a)

$y\ =\ 2x-5$

b)

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

c)

$y\ =\ -2x+3$

5.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

6.

Select all the TRUE statements about the linear function.

a)

The slope of the line is undefined.

b)

The slope of the line is zero.

c)

The equation of the line is y = -1

d)

The equation of the line is x = -1

7.

TRUE OR FALSE: This line has an undefined slope.

a)

true

b)

false

8.

Write the equation of the line.

a)

$y=-\frac{3}{5}x-1$

b)

$y=\frac{3}{5}x-1$

c)

$y=\frac{5}{3}x-1$

d)

$y=-\frac{5}{3}x+1$

9.

Select all the TRUE statements about this linear function.

a)

The domain is all real numbers.

b)

As x decreases, y decreases.

c)

As x increases, y decreases.

d)

$y=-\frac{3}{2}x+4$ is the equation of the line.

e)

The line $y=\frac{2}{3}x$ would be perpendicular to this line.

10.

Select all the TRUE statements about the linear function.

a)

The slope is negative.

b)

The domain is x exists in all real numbers.

c)

The range is y exists in all real numbers.

d)

As x increases, y increases.

e)

The y-intercept is (0, 1).

11.

Describe the transformation from the Absolute Value Parent Function.

a)

Stretches more narrow, shifts up 4 units

b)

Stretches more narrow, shifts down 4 units

c)

Compresses wider, shifts up 4 units

d)

Compresses wider, shifts down 4 units

12.

$y=|\ x\ |+3$

What is the vertex of the absolute value function?

a)

(0,3)

b)

(0, -3)

c)

(3, 0)

d)

(-3, 0)

13.

$y=-|x+2|+5$ What is the range of the function?
*HINT: Sketch a picture before you choose!*

a)

$y\ge5$

b)

$y\le5$

c)

$y\le-2$

d)

$y\ge-2$

14.

What is the equation of the graph below? You can click the picture to zoom in!

a)

$y=-|x+2|-4$

b)

$y=-|x-2|+4$

c)

$y=|x-2|+4$

d)

$y=|x-2|-4$

15.

Use Narrower, Wider, or Same to compare the width of this graph to its parent function.

y = -|x| + 9

a)

Narrower

b)

Wider

c)

Same, but reflected

16.

Select all the TRUE statements about the absolute value function.

a)

As x decreases, y increases.

b)

The vertex of the function is (-3, 2).

c)

$x\ge3$ is the domain.

d)

$y\ge2$ is the range.

e)

This function is steeper than the parent function.

17.

Select all the TRUE statements about the function.

*HINT: Sketch a picture to help you!*

a)

As x increases, y decreases.

b)

This function is reflected from the parent, and shifted down 2 units.

c)

This function's vertex is a minimum.

d)

This function is symmetrical.

e)

This function is more compressed (flatter) than the parent function.

18.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

19.

Choose the correct equation for the graph below.

a)

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

b)

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

c)

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

d)

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

20.

$g(x)=-2|x+4|$

Which transformations from the parent function $f\left(x\right)\ =\ \left|x\right|$ happened to create $g\left(x\right)$ ?

a)

Horizontal translation left 4 units

b)

Horizontal translation right 4 units

c)

Reflection over the x-axis

d)

Vertical stretch by a factor of 2

e)

Vertical translation up 4 units

21.

Select all the TRUE statements about the function.

a)

This function is exponential growth.

b)

The y-intercept is (0, 3)

c)

This function is quadratic.

d)

As x increases, y increases.

22.

Select all the TRUE statements about the function.

a)

This function is exponential growth.

b)

This function is exponential decay.

c)

As x increases, y approaches zero.

d)

As x decreases, y approaches zero.

e)

The y-intercept of the function is $\left(0,\ \frac{1}{5}\right)$

23.

What is the x-intercept of the exponential function?

a)

(0,1)

b)

(0,0)

c)

There is not one

24.

Select all the TRUE statements.

a)

If the common ratio is a fraction between 0 and 1, it is exponential decay.

b)

If the common ratio is greater than 1, it is exponential growth.

c)

The domain for exponential functions is all real numbers.

d)

The range for exponential functions is all real numbers.

25.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

26.

In the graph of this function, as x increases, y ________________.

a)

increases

b)

approaches zero

27.

What is the range of $f\left(x\right)$ ?

$y=2^x-3$
*HINT: Sketch a picture to help you!*

a)

y exists in all real numbers

b)

$y>-3$

c)

$y>0$

d)

$y\le-3$

28.

$f\left(x\right)\ =\ 2^x+1$

What is the equation of the asymptote of $f\left(x\right)$ ?

a)

y = 2

b)

y = 1

c)

y = -1

d)

This function does not have an asymptote.

29.

What is the end behavior of the function?

$f\left(x\right)\ =\ 3^x-5$
*HINT: Sketch a picture to help you!*

a)

As x increases, y decreases. As x decreases, y increases.

b)

As x increases, y decreases. As x increases, y approaches -5.

c)

As x increases, y increases. As x decreases, y approaches -5.

d)

As x increases, y increases. As x decreases, y decreases.

30.

What is the domain of the function shown below?

a)

-2 < x < 5

b)

0 < x < 12

c)

y > 0

d)

All Real Numbers

31.

What is the range of the function shown below?

a)

0 < y < 12

b)

-2 < y < 5

c)

y > 0

d)

All Real Numbers

32.

Which represents exponential decay?

a)

A

b)

B

c)

C

d)

D

33.

a)

$f\left(x\right)\ =\ 2^{\left(x-1\right)}-3$

b)

$f\left(x\right)\ =\ 2^{\left(x+3\right)}-1$

c)

$f\left(x\right)\ =\ 2^{\left(x+1\right)}-3$

d)

$f\left(x\right)\ =\ 2^{\left(x+1\right)}-1$

34.

Select all the true statements about the function.

a)

This function is quadratic.

b)

This function has 2 x-intercepts.

c)

Its vertex is at (1, -6)

d)

The leading coefficient on the equation of this function must be negative.

35.

Select all the TRUE statements.

a)

Point C is a Root or Solution.

b)

Point A is the Vertex.

c)

Point B is an x-intercept.

d)

Point D is the y-intercept.

36.

Select all the TRUE statements about the parabola.

HINT: Sketch a picture to help you!

a)

The vertex is at (-8,-21).

b)

This parabola is more compressed (flatter) than the parent.

c)

The axis of symmetry is at x = -8.

d)

This parabola is downward facing.

e)

This parabola has 2 x-intercepts.

37.

$f\left(x\right)=-3x^2+4$

As x increases, y ______________.

As x decreases, y _______________.

*Sketch it!*

a)

decreases, decreases

b)

decreases, increases

c)

increases, decreases

d)

increases, increases

38.

What is the domain of the function?

a)

D:{ x > 3}

b)

D:{x < 3}

c)

D:{all real numbers}

d)

D:{ -1 < x < 5}

39.

What would this quadratic function be in factored form?

a)

$f\left(x\right)\ =\ \left(x+2\right)\left(x+4\right)$

b)

$f\left(x\right)\ =\ \left(x-8\right)\left(x-4\right)$

c)

$f\left(x\right)\ =\ \left(x-2\right)\left(x+8\right)$

d)

$f\left(x\right)\ =\ \left(x-2\right)\left(x-4\right)$

40.

What is the y-intercept of
f(x)=2x² + 4x + 6

a)

(6 , 0)

b)

(-6 , 0)

c)

(0, -6)

d)

(0 , 6)

41.

Does this function have a maximum or minimum value?

$f\left(x\right)\ =-\frac{1}{3}x^2$

a)

maximum

b)

minimum

42.

Select all the true statements about the function:

$f\left(x\right)\ =\ x^2+5$

a)

5 units left from the parent function.

b)

This function has no solutions.

c)

As x increases, y increases.

d)

This function has 1 solution.

e)

The y-intercept is also the vertex.

43.

Sketch this quadratic function:
A downward facing parabola has a vertex at (-3,2).

Select all the true statements about the function.

a)

The equation must have a negative leading coefficient.

b)

This function has two solutions.

c)

The axis of symmetry is x = -3.

d)

The domain of the function is x exists in all real numbers.

e)

The range is $y\le2$ .

44.

If red represents y = x², which equation represents blue?

a)

y = 2x²

b)

y = -2x²

c)

y = -x²

d)

y = (x - 1)²

45.

Which function matches the graph?

a)

$\left(x\right)\ =\ -\sqrt{x-3}+1$

b)

$f\left(x\right)\ =\ -\sqrt{x+1}+3$

c)

$\left(x\right)\ =\ \sqrt{x+1}+3$

d)

$\left(x\right)\ =\ \sqrt{x+3}-1$

46.

As x increases, y ______________.

a)

increases

b)

decreases

47.

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, and shifted right 5

c)

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

d)

Shifted right 5, shifted down 2

48.

Which of the following is the graph of $y=\left(x-2\right)^3-4$

a)

b)

c)

d)

49.

Which of the following is the graph of $y=-\left(x-4\right)^3+2$

a)

b)

c)

d)

50.

What is the y-intercept of the following cubic function?

a)

(1, 0)

b)

(0, 2)

c)

(-1, 0)

d)

(2, 0)

10-3 Analyzing Functions

Total questions: 50

Worksheet time: 1hrs 21mins

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