Free Printable T1: Functions and Transformation

1.

Determine the range for the function

f(x) = 3(2)^x-4+ 5

a)

[5,∞)

b)

(5,∞)

c)

[4,∞)

d)

(4,∞)

2.

Determine the domain for the function
f(x)=3(2)^x-4+5

a)

[5,∞)

b)

(5,∞)

c)

(-∞,∞)

d)

(∞,-∞)

3.

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

a)

Vertically stretched by a factor of 2, right 3, and up 1

b)

Vertically compressed by a factor of 1/2, left 3 and down 1

c)

Vertically compressed by a factor of 1/2, right 3, and down 1

d)

Vertically stretched by a factor of 2, left 3, and up 1

4.

Describe the transformation of the graph y = -2(x + 5)³

a)

Shrink by 2, Reflected over y-axis, Right 5

b)

Stretch by 2, Reflected over x-axis, Left 5

c)

Stretch by 2, Reflected over x-axis, Right 5

d)

Shrink by 2, reflected over y-axis, Left 5

5.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

6.

What is the horizontal asymptote for the graph of
f(x)=-2(3)^x+4-8 ?

a)

y=8

b)

y=-8

c)

x=-8

d)

x=-4

7.

Which is the equation of the function shown?

a)

$f\left(x\right)=\frac{1}{x+4}+3$

b)

$f\left(x\right)=\frac{1}{x-4}-3$

c)

$f\left(x\right)=\frac{1}{x-3}-4$

d)

$f\left(x\right)=\frac{1}{x+3}+4$

8.

Which of the following represents the graph below?

a)

b)

c)

d)

9.

What is the domain for the following function?

a)

All real numbers except 2.

b)

All real number except -2.

c)

All real numbers except 4.

d)

All real numbers.

10.

What is the range for the following function?

a)

All real numbers.

b)

All real numbers except for -2.

c)

All real numbers except for 2.

d)

All real numbers exceptt for 4.

11.

What is the equation of the Vertical Asymptote of $y=\frac{3}{x-4}+2$

a)

$x=2$

b)

$y=2$

c)

$x=4$

d)

$y=4$

e)

No Vertical Asymptote

12.

What is the horizontal asymptote of the function?

a)

y = 7

b)

y = -7

c)

y = 6

d)

y = -6

13.

Determine the equation for the graph.

a)

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

b)

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

c)

$y=2\sqrt{x}$

d)

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

14.

What is the domain of this function?

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

a)

x ≥ 1

b)

x ≤ 1

c)

x ≥ -3

d)

x ≥ -1

e)

x ≤ -3

15.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical compression by a factor of 3

d)

horizontal shift to the left 2 and vertical compression by a factor of 3

16.

a)

horizontal shift to the right 4 and vertical shift down 2

b)

horizontal shift to the left 4 and vertical shift down 2

c)

horizontal shift to the right 4 and vertical shift up 2

d)

horizontal shift to the left 4 and vertical shift up 2

17.

Which of the following parent functions have a range of $\left[0,\infty\right)$ ? Select all that apply.

a)

b)

c)

d)

18.

Which of the following parent functions does not have a domain

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

?

a)

b)

c)

d)

19.

Determine if the function graphed has a maximum or a minimum value and identify that value.

a)

maximum at -1

b)

minimum at -1

c)

maximum at 4

d)

minimum at 4

20.

Which is not true?

a)

The graph is a reflection of the parent funtion $y=\frac{1}{x}$

b)

An equation for the function is $y=\frac{-1}{x-1}$

c)

There is a vertical asymptote at

$x=-1$

d)

There is a horizontal asymptote at $y=0$

21.

Which characteristic is NOT true for the function: $y=\frac{2}{x-8}+6$

a)

The domain is $\left(-\infty,\ -8\right)\cup\ \left(-8,\ \infty\right)$

b)

The range is $\left(-\infty,\ 6\right)\cup\ \left(6,\ \infty\right)$

c)

The graph is stetched vertically

d)

There is a vertical asymptote at $x=8$

22.

Which is the graph of $y=-\frac{1}{x-2}$ ?

a)

b)

c)

d)

23.

Which equation matches the graph?

a)

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

b)

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

c)

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

d)

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

24.

What is the domain?

a)

[-2, 3]

b)

[-2, 3)

c)

(-2, 3]

d)

[-3, 4]

e)

(-3, 4]

25.

What is the range?

a)

$\left(-\infty,\ -3\right]$

b)

$\left[3,\ -\infty\right)$

c)

$\left(-\infty,3\right]$

d)

None of the answer choices

e)

$\left[-3,\ \infty\right)$

26.

What is the domain?

a)

$\left(\infty,-2\right]$

b)

$\left[-2,\ \infty\right)$

c)

[-2,3]

d)

$\left(-\infty,\ -2\right]$

e)

None of the answer choices

27.

What is the range of the function?

a)

[-1, +∞)

b)

(-1,1)

c)

[1.5, +∞)

d)

(-2, 2)

28.

What is the slant (Oblique) asymptote for the equation

f(x) = (x² - 4x + 2)/(x + 3)

a)

y = x -1

b)

y = x -7

c)

y = -7x + 23

d)

y = -2x + 2

29.

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)

30.

What type(s) of asymptotes does this function have? (Check all that apply.)

a)

Vertical

b)

Horizontal

c)

Oblique

31.

What are the equations of the asymptotes of the given graph

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x= -2, y = 1

c)

x=2 and y= -1

d)

x=1, y =2, y = -2

32.

Which of the following represents the graph of $f\left(x\right)=\frac{1}{x^2-16}$ ?

a)

b)

c)

33.

a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

34.

$f\left(x\right)=\frac{x^2-25}{x^2-x-20}$ Identify the hole(s) in the graph.

a)

$x=4$

b)

$x=-4\ AND\ x=5$

c)

$x=5$

d)

$x=-5$

e)

There are no holes

35.

$h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+3\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$

Identify the x-value of the hole(s).

a)

x=0

b)

x=-3

c)

x=6

d)

x=-7

e)

x=3

36.

$f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x-5\right)}$

Select all of the true statements.

a)

A hole occurs where x=3

b)

vertical asymptote at x=3

c)

vertical asymptote at x=5

d)

A hole occurs where x=5

37.

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

38.

What is the x-intercept of $f\left(x\right)=\frac{x^2-2x-15}{x^2-25}?$

a)

x = 5

b)

x = 3

c)

x = -3

d)

x = -5

39.

What is the y-intercept of

f\left(x\right)=\frac{x^2-3x}{x+3}?

a)

y = 3

b)

y = 1

c)

y = 0

d)

y = -2

40.

What is the horizontal asymptote of

f\left(x\right)=\frac{3x+1}{x-5}?

a)

y = 5

b)

y = 3

c)

y = 1

d)

y = 0

41.

What is the x-intercept of

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

?

a)

x = -1

b)

x = 0

c)

x = 1

d)

all real numbers

42.

Which of these is NOT an asymptote on this graph?

a)

x=-3

b)

x=3

c)

y=2

d)

y=-3

43.

What are the domain and range?

a)

Domain: -5 ≤ x < 5

Range: 3 ≤ y < 6

b)

Domain: -5 ≤ x < 5

Range: 0 ≤ y < 6

c)

Domain: -5 < x ≤ 5

Range: 3 ≤ y < 6

d)

Domain: -5 < x ≤ 5

Range: 0 ≤ y < 6

44.

What are the domain and range?

a)

Domain: x ≤ 8

Range: y ≥ -5

b)

Domain: x ≤ 8

Range: y ≥ 3

c)

Domain: x ≥ 8

Range: y ≥ 3

d)

Domain: x ≥ 8

Range: y ≥ -5

45.

What type of function is shown?

a)

Exponential

b)

square root

c)

quadratic

d)

cube root

46.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

47.

What transformations occur in the following function?

a)

right 3, up 2

b)

left 3, up 2

c)

left 3, down 2

d)

right 3, down 2

48.

a)

A.

b)

B.

c)

C.

d)

D.

49.

Which of the following graphs depicts the following exponential function:

f(x) = 2^x- 2

a)

b)

c)

d)

50.

What could the equation of the exponential function in the graph be?

a)

y = 2^x + 2

b)

y = (1/2)^x + 2

c)

y = 1/2(4)^x + 2

d)

y = 2^x - 2

51.

What is the equation for this graph?

a)

y=3(2)^x

b)

y=2(3)^x

c)

y=4(2)^x

d)

y=2(5)^x

52.

What is the horizontal asymptote?

a)

y =2

b)

y =-2

c)

x=-2

53.

What is the range of the function?

a)

$\left(0,\ \infty\right)$

b)

$\left(-\infty,0\right)$

c)

all real numbers

54.

Which statement is true about the function shown in the graph?

a)

The function is a growth and reflected

b)

The function is a growth and not reflected

c)

The function is a decay and reflected

d)

The function is a decay and not reflected

55.

Which statement is true about the function shown in the graph?

a)

The function is a growth and reflected

b)

The function is a growth and not reflected

c)

The function is a decay and reflected

d)

The function is a decay and not reflected

56.

What is the domain of the graph of $f\left(x\right)\ =\ 6\left(0.25\right)^x$ ?

a)

All real numbers

b)

x > 0

c)

y > 0

d)

x > 6

57.

Which graph is representative of the equation?

a)

b)

c)

d)

58.

Which exponential equation could represent the graph shown?

a)

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

b)

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

c)

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

d)

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

59.

a)

$y=x$

b)

$y=\sqrt{x}$

c)

$y=\left|x\right|$

d)

$y=x^2$

60.

Which equation best describes the graph?

a)

y = 2^-x - 1

b)

y = -2^x + 1

c)

y = -2^x -1

d)

y = 2^-x -1

T1: Functions and Transformation

Total questions: 60

Worksheet time: 3600secs

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