AnswersAlgebra IIFunctions: Part Four

Practice Test Answers

19 verified answers
1
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If she orders 75 shirts and passes the cost along to the employees, what would each employee owe for the shirt if each pays the same amount? Round to the nearest cent.

A
7 point 5 3 dollars
B
7 point 4 0 dollars
C
7 point 4 7 dollars
D
7 point 6 6 dollars
2
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Which graph shows the solution to the equation? log sub 3 of open paren x plus 2 close paren is equal to 1

A
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma 1).
B
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (1 comma 1) and increases as x increases. There is a line parallel to the x axis and cuts the y axis at (0 comma 1).
C
Image with description Coordinate plane with x-axis and y-axis. A logarithmic-shaped curve begins near the y-axis at x equals 0 and extends to the right. The curve passes through 1 comma 0, rises gradually through approximately 3 comma 1 and 9 comma 2, and continues increasing as x increases. A horizontal line y equals negative 1 extends across the graph with arrows on both ends. The curve intersects the horizontal line near 0.3 comma negative 1 and lies above the line for x values greater than this point. Both the curve and the horizontal line continue indefinitely as indicated by arrows.
D
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma negative 1).
3

The equation of the piecewise defined function f of x is shown. What is the value of f of negative 2 ? f of x equals enlarged left-brace first row negative x squared comma x less than negative 2. Second row 3 comma negative 2 less than or equal to x less than 0. Third row 3 x plus 2 comma x greater than or equal to 0.

A
f of negative 2 is equal to negative 4
B
f of negative 2 is equal to negative 6
C
f of negative 2 is equal to 3
D
f of negative 2 is equal to 0
4

What is the range of y is equal to log sub 2 of open paren x minus 6 close paren ?

A
all real numbers not equal to 0
B
all real numbers less than 6
C
all real numbers
D
all real number greater than 6
5

What is the range of the function f of x is equal to negative 2 times open paren 6 to the x th power close paren plus 3 ?

A
left bracket 3 comma infinity right parenthesis
B
left bracket negative 2 comma infinity right parenthesis
C
left parenthesis negative infinity comma negative 2 right bracket
D
open paren negative infinity comma 3 close paren
6

The two expressions have the same value when rounded to the nearest hundredth. the log base 5 of b the log base 9 of 48 What is the approximate value of log b to the nearest hundredth?

A
9 point 1 6
B
0 point 9 3
C
65 point 5 3
D
1 point 2 3
7

What are the domain and range of f of x is equal to the log of open paren x minus 1 close paren plus 2 ?

A
domain: all real numbers; range: all real numbers
B
domain: x is greater than 1 ; range: all real numbers
C
domain: x is greater than 1 ; range: y is greater than 2
D
domain : all real numbers; range: y is greater than 1
8

Two different radioactive isotopes decay to 10 percent of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

A
13 days
B
10 days
C
3 days
D
33 days
9

Which function has a horizontal asymptote of y is equal to 3 ?

A
f of x is equal to 3 times open paren 2 to the x th power close paren
B
f of x is equal to 2 times open paren 3 to the x th power close paren
C
f of x is equal to 2 times 4 raised to the x minus 3 power
D
f of x is equal to 2 times open paren 4 to the x th power close paren plus 3
10

Which of the following describes the graph of y is equal to lfloor x minus 2 rfloor ?

A
The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .
B
The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 3 for negative 2 is less than or equal to x comma x is less than negative 1 .
C
The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 3 for negative 2 is less than x comma x is less than or equal to negative 1 .
D
The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .
11

What is the domain of the function y is equal to the natural log of open paren x plus 2 close paren ?

A
x is less than 2
B
x is greater than negative 2
C
x is less than negative 2
D
x is greater than 2
12

What is the solution of the log base x of 729 is equal to 3 ?

A
81
B
9
C
6
D
18
13

Which of the following shows the graph of y is equal to the natural log of open paren negative 2 x close paren ?

A
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant I, crosses the x axis at 0 point 5 comma 0, decreases with x value. It approaches y axis in the quadrant IV.
B
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant II, crosses the x axis at 0 point 5 comma 0, decreases with the increased value of x. It approaches y axis in the quadrant III.
C
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant II, crosses the x axis at point negative 4 comma 0, decreases with the increased value of x. It approaches y axis in the quadrant III.
D
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant I, crosses the x axis at point 4 comma 0, decreases with x value. It approaches y axis in the quadrant IV.
14

One brand of vinegar has a pH of 4 point 5 Another brand has a pH of 5 point 0 The equation for the pH of a substance is pH is equal to negative log times open bracket cap h raised to the plus power close bracket , where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A
6 point 8 times 10 to the 4th power
B
3 point 2 times 10 inverse
C
3 point 2 times 10 to the 1th power
D
2 point 2 times 10 to the negative 5 power
15

What is the solution of the natural log of open paren x plus 6 close paren minus natural log 9 is equal to 2 ? Round your answer to the nearest hundredth.

A
x is equal to 72 point 5 0
B
x is equal to 53 point 5 0
C
x is equal to 60 point 5 0
D
x is equal to 66 point 5 0
16

What is log sub 6 e to the f th power rewritten using the power property?

A
log sub 6 of open paren e times f close paren
B
e log sub 6 f
C
f log sub 6 e
D
log sub 6 of open paren e plus f close paren
17

Which statement best compares the graphs of f of x is equal to lfloor x rfloor and f of x is equal to lceil x rceil ?

A
The graph of f of x is equal to lceil x rceil is shifted up compared to the graph of f of x is equal to lfloor x rfloor , and the open and closed circles are the same.
B
The open and closed circles are reversed.
C
The two graphs are exactly the same.
D
The graph of f of x is equal to lceil x rceil is shifted up compared to the graph of f of x is equal to lfloor x rfloor , and the open and closed circles are reversed.
18

Which expression is equivalent to log sub 2 9 x cubed ?

A
3 log sub 2 9 minus the log base 2 of x
B
the log base 2 of x plus 3 log sub 2 9
C
3 log sub 2 x minus the log base 2 of 9
D
the log base 2 of 9 plus 3 log sub 2 x
19

The intensity, or loudness, of a sound can be measured in decibels d cap b , according to the equation cap i times d cap b is equal to 10 log open bracket the fraction with numerator cap i and denominator cap i sub 0 close bracket , where cap i is the intensity of a given sound and cap i sub 0 is the threshold of hearing intensity. What is the intensity, in decibels, open bracket cap i times d cap b close bracket , when cap i is equal to 10 to the 32th power times open paren cap i sub 0 close paren ?

A
32
B
737
C
320
D
15

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