AnswersMathematics IIIComparing Characteristics of Functions

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1
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Which statements accurately compare the functions on the graph? Choose two correct answers.

A
The square root and quadratic function share a y -intercept.
B
The square root and absolute value function share an x -intercept.
C
The range of the square root and absolute value function are the same.
D
The quadratic function and the absolute value function have a minimum while the square root function has a maximum.
E
The range of the square root and quadratic function are the same.
2
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Which characteristics do the functions have in common? Choose three correct answers.

A
maximum
B
range
C
y -intercept
D
domain
E
x -intercept
4

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 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).
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 a parabola that opens up with a vertex at the origin. It passes through (negative 2 comma 3) and (2 comma 3).
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-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).
5

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

Which function has a range limited to only negative numbers?

A
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.
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 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 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.
7

Which function has the greatest maximum range value?

A
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.
B
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).
C
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).
D
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).
8

Which function has the greatest x -intercept?

A
j times x is equal to negative 5 times open paren x minus 2 close paren squared
B
g of x is equal to start absolute value x plus 3 end absolute value
C
f of x is equal to 3 x minus 9
D
h of x is equal to 2 to the x th power minus 16
9

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
10

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. 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.
B
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.
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. The graph has a smooth curve that starts from (0 comma 0 point 5), goes up, and passes through (1 comma 1).
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 parabola that opens up, with a vertex at (2 comma 0). It passes through (0 comma 4) and (4 comma 4).

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