Name:     ID: 
 
Email: 

Transformations and Inverses Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Points from a rational function are shown in the table below. 

x
f(x)
-4
1.8333
-3
1.75
-2
1.5
-1
Undefined
0
2.5
1
2.25
2
2.1667

Based on the information in the table, which of the following statements is NOT true about the function?
A.
The x-intercept is (-1, 0)
B.
The vertical asymptote is x = -1.
C.
The y-intercept if (0, 2.5).
D.
The horizontal asymptote is y = 2.
 

 2. 
Which of the following represents f-1(x), the inverse of the function f(x) = –3(4x – 1)2 +3?
A.
f-1(x) = mc002-1.jpg
B.
f-1(x) = mc002-2.jpg
C.
f-1(x) = mc002-3.jpg
D.
f-1(x) = mc002-4.jpg
 

 3. 
Which of the following is not an exponential growth function?
A.
h(x) = (1.25)x
B.
h(x) = (1 – 0.2)x + 3
C.
g(x) = mc003-1.jpg – 12
D.
g(x) = (1 + 0.3)x – 7
 

 4. 
The graph of f(x) is shown below.

mc004-1.jpg

Which of the following is a graph of the inverse of f(x)?
A.
mc004-2.jpg
B.
mc004-3.jpg
C.
mc004-4.jpg
D.
mc004-5.jpg
 

 5. 
These two functions are represented on the graph: g(x) = 23x – 1 and h(x) = mc005-1.jpg. Which of the attributes is the same for both functions?

mc005-2.jpg
A.
Range
B.
Domain
C.
Horizontal asymptote
D.
Vertical asymptote
 

 6. 
Look at the graph below.

mc006-1.jpg

Which of the following represents the vertical and horizontal asymptotes?
A.
x = 3
y = 5
B.
x = 5
y = 0
C.
x = 5
y = 3
D.
x = 0
y = 5
 

 7. 
Points from the exponential function g(x) =  mc007-1.jpg are shown in the table below. Which of the following statements is NOT true about the function?

x
y
-1
32
0
16
1
8
2
4
3
2
4
1

A.
The function is a vertical stretch from the function f(x) = mc007-2.jpg
B.
The horizontal asymptote of the function is y = 16.
C.
The function is exponential decay.
D.
The y-intercept of the function is (0, 16).
 

 8. 
Identify the function that was transformed from the exponential function f(x) = (2)x by reflecting it over the x-axis and translating it down 5 units.
A.
g(x) = (2)–x – 5
B.
g(x) = –(2)x – 5
C.
g(x) = (2)–x – 5
D.
g(x) = –(2)x – 5
 

 9. 
Which of the following represents f-1(x), the inverse of the function f(x) = mc009-1.jpgx + 8?
A.
f-1(x) = 2(x – 8)
B.
f-1(x) = mc009-2.jpg
C.
f-1(x) = mc009-3.jpg
D.
f-1(x) = 2(x + 8)
 

 10. 
The function f(x) = mc010-1.jpg is transformed by the function f(x) =  mc010-2.jpg. Which of the following describes the transformations?
A.
vertical stretch by a factor of 3
horizontal shift right 5 units
vertical shift down 1 unit
B.
vertical stretch by a factor of 3
horizontal shift left 5 units
vertical shift up 1 unit
C.
vertical stretch by a factor of 3
horizontal shift left 5 units
vertical shift down 1 unit
D.
vertical compression by a factor of 3
horizontal shift left 5 units
vertical shift down 1 unit
 

 11. 
The table below contains values of the function f(x).

x
f(x)
-1
-8
0
-5
1
-2
2
1

Which of the following tables represents the inverse of f(x)?
A.
mc011-1.jpg
B.
mc011-2.jpg
C.
mc011-3.jpg
D.
mc011-4.jpg
 

 12. 
The function g(x) = –(0.5)x + 4 is represented in the graph below.

mc012-1.jpg

Which of the following best describes the domain and range of the given function?
A.
The domain is –¥ < x < ¥, and the range is –¥ < g(x) < ¥.
B.
The domain is –¥ < x < ¥, and the range is –¥ < g(x) £ 3.
C.
The domain is –4 < x < 8, and the range is –12 < g(x) £ 8.
D.
The domain is –¥ < x < ¥, and the range is –¥ < g(x) < 4.
 

 13. 
The graph of f(x) is shown below.

mc013-1.jpg

The list below shows possible domain restrictions for f(x).

I. x > 3
II. x < 3
III. x > 0
IV. x < 0

How should the domain be restricted to ensure the inverse of f(x) is a function?
A.
I and II only
B.
III and IV only
C.
III only
D.
IV only
 

 14. 
Look at the graph below.

mc014-1.jpg

Which of the graphs below represents the graph of the inverse of the function?
A.
mc014-2.jpg
B.
mc014-3.jpg
C.
mc014-4.jpg
D.
mc014-5.jpg
 

 15. 
Which of the following statements is true about the function and the inverse of the function graphed below?

mc015-1.jpg
A.
f(x): x-intercept (9, 0); y-intercept (-3, 0)
f-1(x): x-intercept (0, 9); y-intercept 0, -3)
B.
f(x): x-intercept (9, 0); y-intercept (0, -3)
f-1(x): x-intercept (-3, 0); y-intercept (0, 9)
C.
f(x): x-intercept (0, 9); y-intercept (9, 0)
f-1(x): x-intercept (-3, 0); y-intercept (-3, 0)
D.
f(x): x-intercept (9, 0); y-intercept (0, 9)
f-1(x): x-intercept (-3, 0); y-intercept 0, -3)
 

 16. 
Look at the function below.
mc016-1.jpg

Which of the following represents the domain and range of the function?
A.
{x | x Îÿ, x ¹ 5}
{y | y Îÿ, y ¹ 0}
B.
{x | x Îÿ, x ¹ 0}
{y | y Îÿ, y ¹ -5}
C.
{x | x Îÿ, x ¹ 0}
{y | y Îÿ, y ¹ 5}
D.
{x | x Îÿ, x ¹ -5}
{y | y Îÿ, y ¹ 0}
 

 17. 
The graph of f(x) is shown below.

mc017-1.jpg

Which of the following points would be contained in the inverse of f(x)?
A.
(-6, -3)
B.
(-3, -6)
C.
(-3, 6)
D.
(6, 3)
 

 18. 
Look at the table below.

x
y
-1
32
0
12
1
0
2
-4
3
0
4
12

Which of the following tables represents the inverse of the function?
A.
mc018-1.jpg
B.
mc018-2.jpg
C.
mc018-3.jpg
D.
mc018-4.jpg
 

 19. 
Look at the graph below.

mc019-1.jpg

Which of the following statements is true about the function shown on the graph?
A.
g(x) is the inverse of f(x).
B.
f(x) reflected across the line of reflection, y = x, is g(x).
C.
g(x) is a function.
D.
The domain of f(x) and the range of g(x) do not contain the same values.
 

 20. 
Look at the graphs below.

mc020-1.jpg

Which of the following attributes is the same for both functions?
A.
Domain
B.
Range
C.
x-intercept
D.
None of these are the same.
 



 
         Start Over