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Exponential and Logarithmic Functions — Test Answers

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

The x -intercept of f inverse of x is the same as the y -intercept of f of x .

The x -intercept of f inverse of x is the opposite of the y -intercept of f of x .

The slope of f inverse of x is the same as the slope of f of x .

The slope of f inverse of x is the opposite of the slope of f of x .

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Which function is shown in the graph?

y is equal to 1 half raised to the x plus 1 power minus 3

y is equal to 1 half raised to the x minus 1 power plus 3

y is equal to 1 half raised to the x minus 3 power plus 1

y is equal to 1 half raised to the x plus 3 power minus 1

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

company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year

company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year

company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year

company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year

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

8 point 2 3 2 , Graph A

8 point 7 5 6 , Graph B

9 point 2 1 3 , Graph A

negative 8 point 2 3 2 , Graph B

What is the decay factor of this data?

Decay factor is 0 point 0 5

Decay factor is negative 1 point 5

Decay factor is 14 point 2 5

Decay factor is 0 point 9 5

Which statement is true?

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 .

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 .

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 .

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 .

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

y is equal to 9 x squared ; each y -value is the previous y -value plus 9 more than was added previously.

y is equal to 9 x ; each y -value is the previous y -value plus 9 .

y is equal to 9 to the x th power ; each y -value is the previous y -value multiplied by another 9 .

y is equal to x to the 9th power ; each y -value is the previous y -value multiplied by 9 .

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

negative 27 negative 40 point 5

12 8

negative 27 40 point 5

27 40 point 5

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

the graph is three dimensional

the graph will rise or fall more dramatically than a polynomial graph

the exponent in the equation is less than one

the graphs represent the population of bacteria in your mouth

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

all real numbers greater than negative 3

all real numbers greater than 3

all real numbers less than 3

all real numbers less than negative 3

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

b is less than 0 and b is equal to 1

b is greater than 0 and b is equal to 1

b is greater than 0 and b is not equal to 1

b is less than 0 and b is not equal to 1

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

y is equal to 2 times open paren 5 to the x th power close paren

y is equal to 5 raised to the x plus 2 power

y is equal to 2 to the x th power

y is equal to 5 to the x th power plus 2

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?

46 point 6 days

2 point 5 days

5 point 0 days

66 point 7 days

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.

f inverse of x has a range of all real numbers.

f inverse of x has a y - intercept of open paren 0 comma negative 36 close paren .

f inverse of x has a restricted domain.

f inverse of x has a slope of negative 2 thirds .

f inverse of x has an x - intercept of open paren negative 36 comma 0 close paren .

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?

Calvin invests his money 2 years longer.

Makayla invests her money 2 years longer.

Calvin invests his money 1 year longer.

Makayla invests her money 1 year longer.

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?

Decay factor is 9 ; y -intercept is 0 point 7 7

Growth factor is 9 ; y -intercept is 0 point 7 7

Growth factor is 0 point 7 7 ; y -intercept is 9

Decay factor is 0 point 7 7 ; y -intercept is 9

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

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'

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'

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'

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'

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'

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 ?

Translate each point of the graph of h x 3 units up.

Translate each point of the graph of h x 3 units down.

Translate each point of the graph of h x 3 units left.

Translate each point of the graph of h x 3 units right.

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

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.

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.

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.

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.

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

S-shaped graph

J-shaped graph

T-shaped graph

straight horizontal line

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