AnswersMathematics IIComparing Characteristics of Functions

Comparing Characteristics of Functions — Quiz Answers

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Consider the y -intercepts of the functions. f of x is equal to 1 fifth divides x minus 15 divides g of x is equal to open paren x minus 2 close paren squared

Answer:

-15|4

42
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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 first quadrant.
B
The minimum of h of x is farther right and up from the minimums of f of x and g of x .
C
The minimum of h of x is farther left and down from the minimums of f of x and g of x .
D
The minimums of g of x and h of x are both in the third quadrant.
43

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 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).
B
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.
C
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).
D
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.
44

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 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).
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 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).
45

Which statements can be used to compare the characteristics of the functions? Choose two correct answers.

A
All three functions share the same domain.
B
f of x has an all negative domain.
C
h of x has a range of all negative numbers.
D
All three functions share the same range.
E
g of x has the greatest maximum value.
46

Which function has exactly one x - and y -intercept?

A
Image with description On a coordinate plane, the x-axis ranges from negative 10 to 6 by 2, and the y-axis ranges from negative 6 to 10 by 2. The graph has a smooth curve that starts from (0 comma 0 point 5), goes up, and passes through (1 comma 1).
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 parabola that opens up, with a vertex at (2 comma 0). It passes through (0 comma 4) and (4 comma 4).
C
Image with description On a coordinate plane, the x-axis ranges from negative 10 to 6 by 2, and the y-axis ranges from negative 6 to 10 by 2. A smooth curve approaches the x-axis in the negative direction, passes through (0 comma 1), and has a vertical asymptote at x equals 2.
D
Image with description On a coordinate plane x lists from negative 6 to 10 by 2 and y axis lists from negative 8 to 8 by 2. The graph has two lines forming V shape and its vertex is at (2 comma negative 2). One line passes through (5 comma 0) and extends infinitely through the first quadrant. The other line passes through (0 comma 1) and extends infinitely through the second quadrant.
47

Which statement accurately compares the annual change in production to the annual change in average salary?

A
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.
B
The annual changes cannot be compared because the initial production value is unknown.
C
The annual change in production has exceeded the annual change in the average salary.
D
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.
48

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 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).
D
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.
49

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

A
x -intercept
B
range
C
y -intercept
D
maximum
E
domain
50

Consider the function. g of x is equal to square root of x plus 4 end root minus 6 Which function has the same y -intercept as this function?

A
f of x is equal to the fraction with numerator 4 and denominator x minus 8 minus 3 point 5
B
f of x is equal to 2 divides x plus 2 divides
C
f of x is equal to negative 4 over x minus 1
D
f of x is equal to start absolute value x minus 4 end absolute value
51

How do the functions in the table compare?

A
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.
B
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.
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 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.
52

Consider the function. g of x is equal to square root of x plus 4 end root minus 6 Which function has the same y -intercept as this function?

A
f of x is equal to the fraction with numerator 4 and denominator x minus 8 minus 3 point 5
B
f of x is equal to start absolute value x minus 4 end absolute value
C
f of x is equal to 2 divides x plus 2 divides
D
f of x is equal to negative 4 over x minus 1
53

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

A
The x -intercept in function B is three times as large as the x -intercept in function A.
B
The x -intercept in function B is one-third as large as the x -intercept in function A.
C
The distance between the x -intercepts in function A is twice the distance between the x -intercepts of function B.
D
The distance between the x -intercepts in function A is half the distance between the x -intercepts of function B.
54

Consider the function. g of x is equal to square root of x plus 4 end root minus 6 Which function has the same y -intercept as this function?

A
f of x is equal to negative 4 over x minus 1
B
f of x is equal to 2 divides x plus 2 divides
C
f of x is equal to start absolute value x minus 4 end absolute value
D
f of x is equal to the fraction with numerator 4 and denominator x minus 8 minus 3 point 5
55

Which statements can be used to compare the functions? Choose two correct answers.

A
Only f of x has an x -intercept.
B
g of x has the greatest maximum.
C
All three functions have the same range values.
D
All three functions have a y -intercept.
E
All three functions have the same domain values.
56

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

A
The minimum of h of x is farther left and down from the minimums of f of x and g of x .
B
The minimum of h of x is farther right and up from the minimums of f of x and g of x .
C
The minimums of g of x and h of x are both in the first quadrant.
D
The minimums of g of x and h of x are both in the third quadrant.
57

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

A
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).
B
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).
C
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).
D
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.
58

Which statement compares the ranges of the functions?

A
The ranges of both f of x and g of x are limited to y is less than or equal to negative 1 .
B
Since the range of f of x is limited to y is greater than or equal to negative 4 and the range of g of x is limited to y is less than or equal to 0 , the ranges overlap for the values negative 4 is less than or equal to y comma y is less than or equal to 0 .
C
Since the range of f of x is limited to y is less than or equal to 0 and the range of g of x is limited to y is greater than or equal to negative 4 , the ranges overlap for the values negative 4 is less than or equal to y comma y is less than or equal to 0 .
D
The ranges of both f of x and g of x are limited to y is greater than or equal to negative 1 .
59

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
f of x is equal to negative 2 times open paren x minus 8 close paren squared
B
h of x is equal to negative 5 divides x divides plus 10
C
j times x is equal to negative 4 times open paren x plus 2 close paren squared plus 8
D
m times x is equal to 1 fourth divides x minus 8 divides plus 6
E
k times x is equal to 1 fourth times open paren x minus 4 close paren squared plus 4
60

Which statements can be used to compare the characteristics of the functions? Choose two correct answers.

A
All three functions share the same domain.
B
f of x has an all negative domain.
C
h of x has a range of all negative numbers.
D
All three functions share the same range.
E
g of x has the greatest maximum value.

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