AnswersMathematics IIComparing Characteristics of Functions

Comparing Characteristics of Functions — Quiz Answers

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Which functions have a y -intercept that is greater than the y -intercept of the function g of x is equal to start absolute value x plus 3 end absolute value plus 4 ? Choose three correct answers.

A
k times x is equal to 1 fourth times open paren x minus 4 close paren squared plus 4
B
j times x is equal to negative 4 times open paren x plus 2 close paren squared plus 8
C
f of x is equal to negative 2 times open paren x minus 8 close paren squared
D
h of x is equal to negative 5 divides x divides plus 10
E
m times x is equal to 1 fourth divides x minus 8 divides plus 6
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Which statement accurately compares the annual change in production to the annual change in average salary?

A
The annual change in production has exceeded the annual change in the average salary.
B
The annual changes cannot be compared because the initial production value is unknown.
C
The annual change in production increases at a slower rate, 105 percent per year, than the annual increase in average salary, 500 dollars per year.
D
The annual change in production increases at a slower rate, 5 percent per year, than the annual increase in the average salary, 500 dollars per year.
63

Which function has the greatest maximum range value?

A
Image with description On a coordinate plane, the x-axis ranges from negative 6 to 10 by 2, and the y-axis ranges from negative 8 to 8 by 2. The graph has a parabola that opens down with a vertex (3 comma 1) and passes through (2 comma 0) and (4 comma 0).
B
Image with description On a coordinate plane, the x and y axes range from negative 10 to 6 by 2. A smooth curve that approaches the negative direction of the x-axis, passes through (0 comma negative 1), goes down, and passes through (2 comma negative 4).
C
Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 in increments of 2. A smooth curve originates from (negative 3 comma 3), goes down, and passes through (2 comma 1) and (7 comma 0).
D
Image with description On a coordinate plane, the x and y axes range from negative 10 to 6 in increments of 2. The graph has an inverted v-shaped draw-up with a vertex at (negative 3 comma 1). One line passes through (negative 5 comma negative 1) and extends infinitely into the third quadrant. The other line passes through (0 comma negative 2) and extends infinitely into the fourth quadrant.
64

Which statement compares the relative locations of the minimums of the functions?

A
The minimums of g of x and h of x are both in the third quadrant.
B
The minimums of g of x and h of x are both in the first quadrant.
C
The minimum of h of x is farther right and up from the minimums of f of x and g of x .
D
The minimum of h of x is farther left and down from the minimums of f of x and g of x .
65

Which function has a domain and range that includes all real values?

A
Image with description On a coordinate plane, the x-axis ranges from negative 6 to 10 in increments of 2, and the y-axis ranges from negative 6 to 10 by 2. A smooth curve starts from (2 comma 2), goes up, and passes through (6 comma 4).
B
Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 in increments of 2. The graph has an inverted v-shaped curve with a vertex at the origin. One line extends infinitely into the third quadrant passing through (negative 4 comma negative 4). The other line extends infinitely into the fourth quadrant passing through (4 comma negative 4).
C
Image with description On a coordinate plane, the x-axis ranges from negative 6 to 10 in increments of 2, and the y-axis ranges from negative 10 to 8 in increments of 2. The graph has a straight line with a positive slope, goes through (0 comma negative 4), and (2 comma 0). It extends infinitely in both directions.
D
Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 in increments of 2. The graph has a parabola that opens up with a vertex at the origin. It passes through (negative 2 comma 3) and (2 comma 3).
66

How do the x -intercepts of the two functions compare?

A
The x -intercept in function B is one-third as large as the x -intercept in function A.
B
The distance between the x -intercepts in function A is twice the distance between the x -intercepts of function B.
C
The x -intercept in function B is three times as large as the x -intercept in function A.
D
The distance between the x -intercepts in function A is half the distance between the x -intercepts of function B.
67

Which function has a range limited to only negative numbers?

A
Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 by 2. A straight line with a negative slope passes through (negative 3 comma 0) and (0 comma negative 3). It extends infinitely in both directions.
B
Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 by 2. The graph has a smooth curve that starts from (negative 2 comma 1), goes down into the fourth quadrant, and passes through (7 comma negative 2).
C
Image with description On a coordinate plane, the x-axis ranges from negative 8 to 8 by 2, and the y-axis ranges from negative 10 to 4 by 2. The graph has a draw-up in the shape of an inverted v with a vertex at (2 negative 1). One line passes through (0 comma negative 3) and extends infinitely into the third quadrant. The other line passes through (4 comma negative 3) and extends infinitely into the fourth quadrant.
D
Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 in increments of 2. A parabola opens up and passes through (negative 3 comma 1) and (negative 1 comma 1). Its vertex is at (negative 2 comma negative 3).
68

How do the functions in the table compare?

A
Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
B
Since x -intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
C
Since y -intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
D
Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
69

Which characteristics do the functions have in common? Choose three correct answers.

A
range
B
y -intercept
C
domain
D
maximum
E
x -intercept

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