AnswersCA-Algebra I A – 6002Exponential Functions with Radical Bases

Exponential Functions with Radical Bases Answers

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1
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Which is equivalent to ?

Question illustration
A
125 Superscript one-third x
Option A
B
125 Superscript StartFraction 1 Over 3 x EndFraction
Option B
C
125 Superscript 3 x
Option C
D
125 Superscript (one-third) SuperSuperscript x
Option D
2
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5

Which expression is equivalent to ?

Question illustration
A
3 RootIndex 3 StartRoot 3 EndRoot
Option A
B
3 RootIndex 3 StartRoot 3 cubed EndRoot
Option B
C
9 RootIndex 3 StartRoot 3 EndRoot
Option C
D
27 RootIndex 3 StartRoot 3 EndRoot
Option D
6

Which graph represents the function ?

A
[Image: On a coordinate plane, an exponential function cro...]
Option A
B
[Image: On a coordinate plane, an exponential function app...]
Option B
C
[Image: On a coordinate plane, an exponential function dec...]
Option C
D
[Image: On a coordinate plane, an exponential function app...]
Option D
7

Which exponential functions have been simplified correctly? Check all that apply.

A
f (x) = 5 RootIndex 3 StartRoot 16 Endroot Superscript x Baseline = 5 (2 RootIndex 3 StartRoot 2 EndRoot) Superscript x
Option A
B
f (x) = 2.3 (8) Superscript one-half x Baseline = 2.3 (4) Superscript x
Option B
C
f (x) = 81 Superscript StartFraction x Over 4 EndFraction Baseline = 3 Superscript x
Option C
D
f (x) = three-fourths StartRoot 27 EndRoot Superscript x Baseline = three-fourths (3 StartRoot 3 EndRoot) Superscript x
Option D
E
f (x) = (24) Superscript one-third x Baseline = 2 (RootIndex 3 StartRoot 3 EndRoot) Superscript x
Option E
8

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9

How are the functions and related?

A
The output values of g(x) are one-half the output values of f(x) for the same value of x.
B
The output values of g(x) are one-quarter the output values of f(x) for the same value of x.
C
The output values of g(x) are the square root of the output values of f(x) for the same value of x.
D
The output values of g(x) are the square of the output values of f(x) for the same value of x.
10

⇒ 4

Answer:

78924

11

Determine the domain and range of the function .

A
{x| all real numbers}; {y| y > 0}
B
{x| all real numbers}; {y| y ≥ 0}
C
{x| x > 0}; {y| all real numbers}
D
{x| x ≥ 0}; {y| all real numbers}
12

Simplify the function . Then determine the key aspects of the function. The initial value is . The simplified base is . The domain is . The range is .

Answers:
Selection 1:1/3
Selection 2:27
Selection 3:all real numbers
Selection 4:y > 0
13

Explain why the square root of a number is defined to be equal to that number to the 1/2 power.

Answer:

The square root of a number and squaring a number are inverse operations. If we represent the square root of x as x to the power of 'n', then $(\sqrt{x})^2 = (x^n)^2 = x^1$. According to the power of a power rule, $(x^n)^2 = x^{2n}$. Therefore, $2n = 1$, which means $n$ must be $1/2$. Thus, the square root of a number is equal to that number raised to the $1/2$ power.

14

Determine which function produces the same graph as .

Question illustration
A
f(x) = 4x
B
f(x) = 42x
C
f(x) = 83x
D
f(x) = 162x
15

What did you include in your response? Check all that apply.

A
Use the power of a power rule to multiply the exponents.
B
The product of the exponents must be 1.
C
The exponents are reciprocals.

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