AnswersAdv. Algebra II S2 OriginalSimplifying Rational Expressions

Graphing Exponential Functions Answers

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1
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Which set of ordered pairs could be generated by an exponential function?

A
(1, 1), , ,
Option A
B
(1, 1), , ,
Option B
C
, , ,
Option C
D
, , ,
Option D
2
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Which of the following describes the transformation of from the parent function ?

Question illustration
A
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
B
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
C
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
D
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up
3

Which statement best describes the domain and range of f(x) = –(7)x and g(x) = 7x?

A
f(x) and g(x) have the same domain and the same range.
B
f(x) and g(x) have the same domain but different ranges.
C
f(x) and g(x) have different domains but the same range.
D
f(x) and g(x) have different domains and different ranges.
4

Which properties are present in a table that represents an exponential function in the form when ?I. As the x-values increase, the y-values increase.II. The point (1, 0) exists in the table.III. As the x-values increase, the y-values decrease.IV. As the x-values decrease, the y-values decrease, approaching a singular value.

Question illustration
A
I and IV
B
I and II
C
II and III
D
III only
5

Which table represents an exponential function of the form when ?

Question illustration
A
mc028-3.jpg
Option A
B
mc028-4.jpg
Option B
C
mc028-5.jpg
Option C
D
mc028-6.jpg
Option D
6

Which set of ordered pairs could be generated by an exponential function?

A
, (0, 0), , (2, 1)
Option A
B
(–1, –1), (0, 0), (1, 1), (2, 8)
C
, (0, 1), (1, 2), (2, 4)
Option C
D
(–1, 1), (0, 0), (1, 1), (2, 4)
7

Which graph represents an exponential function?

A
On a coordinate plane, a line curves upwards gradually.
Option A
B
On a coordinate plane, a curve decreases, changes directions, and then decreases again.
Option B
C
On a coordinate plane, a line is level and then curves upwards rapidly.
Option C
D
On a coordinate plane, 2 curves mirror each other in quadrants 1 and 3.
Option D
8

Which graph represents an exponential growth function?

A
On a coordinate plane, a line rapidly decreases and then levels off.
Option A
B
On a coordinate plane, a line increases gradually.
Option B
C
On a coordinate plane, a line decreases gradually.
Option C
D
On a coordinate plane, a line is level and then curves upwards rapidly.
Option D
9

What are the domain and range of the function f(x) = 3x + 5?

A
domain: ; range:
Option A
B
domain: ; range:
Option B
C
domain:; range:
Option C
D
domain: ; range:
Option D
10

Which function is graphed below?

Question illustration
A
y = one-third (3) Superscript x
Option A
B
y = 3 (one-third) Superscript x
Option B
C
y = (one-half) Superscript x Baseline + 2
Option C
D
y = (2) Superscript x Baseline minus 1
Option D
11

What is the product?

Question illustration
A
StartFraction k + 1 Over k squared EndFraction
Option A
B
StartFraction k minus 1 Over k squared EndFraction
Option B
C
StartFraction negative 1 Over k EndFraction
Option C
D
StartFraction 1 Over k EndFraction
Option D
12

Which expression is equivalent to ?

Question illustration
A
StartFraction 1 Over x EndFraction
Option A
B
StartFraction 1 Over x Superscript 5 Baseline EndFraction
Option B
C
StartFraction 1 Over x Superscript 9 Baseline EndFraction
Option C
D
StartFraction 1 Over x Superscript 24 Baseline EndFraction
Option D
13

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = negative 2.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = negative 2.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = 2.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1 , and the other curve opens down and to the left in quadrants 2, 1, and 4. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = 2.
Option D
14

For the inverse variation equation , what is the value of p when V = ?

Question illustration
A
Option
Option A
B
Option
Option B
2
2
3
32
15

What are the vertical and horizontal asymptotes for the function ?

Question illustration
A
vertical asymptote: x = 1horizontal asymptote: none
B
vertical asymptote: x = 1horizontal asymptote: y = 0
C
vertical asymptote: x = –2, x = 3horizontal asymptote: y = 0
D
vertical asymptote: x = –2, x = –3horizontal asymptote: none
16

What is the quotient in simplest form? Assume .

Question illustration
A
Negative StartFraction m Superscript 12 Baseline n Superscript 6 Baseline Over 2 EndFraction
Option A
B
Negative StartFraction m Superscript 27 Baseline n Superscript 8 Baseline Over 2 EndFraction
Option B
C
6 m Superscript 12 Baseline n Superscript 6 Baseline
Option C
D
8 m Superscript 12 Baseline n Superscript 6 Baseline
Option D
17

The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation , where p represents the resistivity of the wire’s material, L represents the length of the wire, and d represents the diameter of the wire. What happens to the resistance of the wire as the diameter approaches 0?

Question illustration
A
The resistance approaches 0.
B
The resistance approaches .
Option B
C
The resistance approaches L.
D
The resistance approaches infinity.
18

Riley makes a mistake in step 2 while doing her homework. What was her mistake? Step 1: Step 2: Step 3: Step 4:

Question illustration
A
She added the two fractions incorrectly.
B
She used the wrong common denominator.
C
She did not distribute the negative correctly.
D
She did not multiply the first fraction by a factor.
19

Which statement is true about the discontinuities of the function f(x)?

Question illustration
T
There is a hole at x = 2.
T
There are asymptotes at x = 0 and x = –1.
T
There are asymptotes at x = 0 and x = –1 and a hole at .
Option T
T
There are holes at x = 0 and x = –1 and an asymptote at x = 2.
20

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using . Which statement is true?

Question illustration
A
The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
B
The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
C
The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
D
The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

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