AnswersAlgebraic ReasoningExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

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Which statement describes the relationship between the function and its inverse?

A
The x -intercept of f inverse of x is the same as the y -intercept of f of x .
B
The x -intercept of f inverse of x is the opposite of the y -intercept of f of x .
C
The slope of f inverse of x is the same as the slope of f of x .
D
The slope of f inverse of x is the opposite of the slope of f of x .
2
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Which function is shown in the graph?

A
y is equal to 1 half raised to the x plus 1 power minus 3
B
y is equal to 1 half raised to the x minus 1 power plus 3
C
y is equal to 1 half raised to the x minus 3 power plus 1
D
y is equal to 1 half raised to the x plus 3 power minus 1
3

If the number of employees is an indicator of a successful business, in which company should Ajay invest?

A
company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year
B
company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year
C
company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year
D
company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year
4

Find the missing value for the exponential function represented by the table. Then select the graph that best fits the equation.

A
8 point 2 3 2 , Graph A
B
8 point 7 5 6 , Graph B
C
9 point 2 1 3 , Graph A
D
negative 8 point 2 3 2 , Graph B
5

What is the decay factor of this data?

A
Decay factor is 0 point 0 5
B
Decay factor is negative 1 point 5
C
Decay factor is 14 point 2 5
D
Decay factor is 0 point 9 5
6

Which statement is true?

A
The second function grows approximately 21 times faster than the first function over the interval 4 is less than x comma x is less than 5 .
B
The second function grows approximately 6 times faster than the first function over the interval 2 is less than x comma x is less than 3 .
C
The second function grows approximately 21 times slower than the first function over the interval 4 is less than x comma x is less than 5 .
D
The second function grows approximately 2 point 5 times slower than the first function over the interval 2 is less than x comma x is less than 3 .
7

Which equation describes the relationship between the variables in the table?

A
y is equal to 9 x squared ; each y -value is the previous y -value plus 9 more than was added previously.
B
y is equal to 9 x ; each y -value is the previous y -value plus 9 .
C
y is equal to 9 to the x th power ; each y -value is the previous y -value multiplied by another 9 .
D
y is equal to x to the 9th power ; each y -value is the previous y -value multiplied by 9 .
8

Find the missing values for the exponential function represented by the table and complete the table.

A
negative 27 negative 40 point 5
B
12 8
C
negative 27 40 point 5
D
27 40 point 5
9

Exponential functions exhibit exponential growth (or decay). What does this mean to the graphs of these functions?

A
the graph is three dimensional
B
the graph will rise or fall more dramatically than a polynomial graph
C
the exponent in the equation is less than one
D
the graphs represent the population of bacteria in your mouth
10

What is the domain of y is equal to log sub 4 of open paren x plus 3 close paren ?

A
all real numbers greater than negative 3
B
all real numbers greater than 3
C
all real numbers less than 3
D
all real numbers less than negative 3
11

Which of the following is true about the base b of a logarithmic function?

A
b is less than 0 and b is equal to 1
B
b is greater than 0 and b is equal to 1
C
b is greater than 0 and b is not equal to 1
D
b is less than 0 and b is not equal to 1
12

The range of which function is open paren 2 comma infinity close paren ?

A
y is equal to 2 times open paren 5 to the x th power close paren
B
y is equal to 5 raised to the x plus 2 power
C
y is equal to 2 to the x th power
D
y is equal to 5 to the x th power plus 2
13

A population of insects increases at a rate of 1 point 5 percent per day. About how long will it take the population to double?

A
46 point 6 days
B
2 point 5 days
C
5 point 0 days
D
66 point 7 days
14

Consider the function. f of x is equal to negative 2 thirds x minus 24 Which conclusions can be drawn about f inverse of x ? Choose two correct answers.

A
f inverse of x has a range of all real numbers.
B
f inverse of x has a y - intercept of open paren 0 comma negative 36 close paren .
C
f inverse of x has a restricted domain.
D
f inverse of x has a slope of negative 2 thirds .
E
f inverse of x has an x - intercept of open paren negative 36 comma 0 close paren .
15

Calvin deposits 400 dollars in a savings account that accrues 5 percent interest compounded monthly. After c years, Calvin has 658 point 8 0 dollars Makayla deposits 300 dollars in a different savings account that accrues 6 percent interest compounded quarterly. After m years, Makayla has 613 point 0 4 dollars What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A
Calvin invests his money 2 years longer.
B
Makayla invests her money 2 years longer.
C
Calvin invests his money 1 year longer.
D
Makayla invests her money 1 year longer.
16

Interpret the following exponential function: y is equal to 9 times 0 point 7 7 to the x th power What is the growth/decay factor? What is the y -intercept?

A
Decay factor is 9 ; y -intercept is 0 point 7 7
B
Growth factor is 9 ; y -intercept is 0 point 7 7
C
Growth factor is 0 point 7 7 ; y -intercept is 9
D
Decay factor is 0 point 7 7 ; y -intercept is 9
17

Which tables could be used to verify that the functions they represent are inverses of each other? Choose two correct answers.

A
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 14'; Column 3, 'negative 10'; Column 4, 'negative 6'; Column 5, '0'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 4'; Column 3, 'negative 2'; Column 4, '0'; Column 5, '3'; Column 6, '5'
B
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 14'; Column 3, 'negative 10'; Column 4, 'negative 6'; Column 5, '0'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, '4'; Column 3, '2'; Column 4, '0'; Column 5, 'negative 3'; Column 6, 'negative 5'
C
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '2'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 4'; Column 3, '0'; Column 4, '6'; Column 5, '10'; Column 6, '14'
D
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '3'; Column 6, '9' Row 2: Column 1, 'y'; Column 2, 'negative 14'; Column 3, 'negative 10'; Column 4, 'negative 6'; Column 5, '0'; Column 6, '4'
E
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '2'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, '4'; Column 3, '0'; Column 4, 'negative 6'; Column 5, 'negative 10'; Column 6, 'negative 14'
18

If you are given the graph of h of x is equal to the log base 6 of x , how could you graph m times x is equal to log sub 6 of open paren x plus 3 close paren ?

A
Translate each point of the graph of h x 3 units up.
B
Translate each point of the graph of h x 3 units down.
C
Translate each point of the graph of h x 3 units left.
D
Translate each point of the graph of h x 3 units right.
19

Which of the following shows the graph of y is equal to 4 to the x th power plus 3 ?

A
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. It passes through the points (3 comma 1) and (4 comma 4). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.
B
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. The curve passes through the points (negative 3 comma 1), (negative 2 comma 4), and (negative 1 point 5 comma, 8). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.
C
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals negative 3 as x approaches negative infinity, indicated by an arrow pointing left along the line y equals negative 3. It passes through the y-intercept (0 comma negative 2). The curve goes through the points (negative 1 comma negative 3), (1 comma 1) and (1 point 5 comma 6). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.
D
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 3 as x approaches negative infinity. It passes through the points (negative 2 comma 3), (0 comma 4) and (1 comma 7). As x increases, the curve rises sharply towards positive infinity. As x decreases, the curve flattens out, approaching the asymptote at y equals 3.
20

On a graph, what characteristic shape is shown by exponential growth?

A
S-shaped graph
B
J-shaped graph
C
T-shaped graph
D
straight horizontal line

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