AnswersAlgebraic ReasoningSquare Root and Absolute Value Functions

Square Root and Absolute Value Functions — Test Answers

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1
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Which equation represents the function graphed on the coordinate plane?

A
g of x is equal to start absolute value x minus 1 end absolute value plus 3
B
g of x is equal to start absolute value x plus 1 end absolute value plus 3
C
g of x is equal to start absolute value x plus 3 end absolute value plus 1
D
g of x is equal to start absolute value x plus 3 end absolute value minus 1
2
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What is the vertex of the absolute value function?

A
open paren 4 comma negative 1 close paren
B
open paren 4 comma 1 close paren
C
open paren 1 comma negative 4 close paren
D
open paren 1 comma 4 close paren
3

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

A
The range of the square root and quadratic function are the same.
B
The quadratic function and the absolute value function have a minimum while the square root function has a maximum.
C
The range of the square root and absolute value function are the same.
D
The square root and quadratic function share a y -intercept.
E
The square root and absolute value function share an x -intercept.
4

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

A
range
B
x -intercept
C
maximum
D
y -intercept
E
domain
5

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

A
All three functions share the same y -intercept.
B
All three functions share the same domain.
C
h of x has the greatest x - intercept.
D
g of x has the smallest minimum value.
E
f of x has the greatest maximum.
6

How do the functions in the tables compare?

A
The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.
B
Since the maximums occurred at the same x -value, the rockets followed the same path.
C
Since the x -intercepts are the same for both functions, the rockets followed the same path.
D
The rockets traveled the same height in the air, but the rocket for group B was in the air for a longer time.
7

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

A
minimum
B
x -intercept
C
range
D
domain
E
y -intercept
8

Which statement is true about f of x is equal to negative 2 thirds start absolute value x plus 4 end absolute value minus 6 ?

A
The graph of f of x has a domain of x is less than or equal to negative 6 .
B
The graph of f of x is a horizontal stretch of the graph of the parent function.
C
The graph of f of x opens upward.
D
The graph of f of x has a vertex of open paren negative 4 comma 6 close paren .
9

What is the domain of the function y is equal to 2 square root of x minus 5 end root ?

A
x is greater than or equal to 2
B
x is greater than or equal to 10
C
x is greater than or equal to negative 5
D
x is greater than or equal to 5
10

Which function has the domain x is greater than or equal to negative 11 ?

A
y is equal to square root of x minus 11 end root plus 5
B
y is equal to square root of x plus 5 end root minus 11
C
y is equal to square root of x plus 11 end root plus 5
D
y is equal to square root of x plus 5 end root plus 11
11

Which equation is the inverse of open paren x minus 4 close paren squared minus 2 thirds is equal to 6 y minus 12 ?

A
y is equal to negative 4 plus or minus square root of 6 x minus 34 thirds end root
B
y is equal to 1 sixth x squared minus 4 thirds x plus 43 ninths
C
negative open paren x minus 4 close paren squared minus 2 thirds is equal to negative 6 y plus 12
D
y is equal to 4 plus or minus square root of 6 x minus 34 thirds end root
12

A company manufactures 16 -oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0 point 1 5 oz, the production is stopped. What is the range of acceptable values for production to continue?

A
15 point 8 5 oz to 16 point 0 0 oz
B
15 point 1 5 oz to 16 point 0 0 oz
C
16 point 1 5 oz to 16 point 4 5 oz
D
15 point 8 5 oz to 16 point 1 5 oz
13

Which equation is the inverse of y is equal to 9 x squared minus 4 ?

A
y is equal to plus or minus square root of x over 9 plus 4 end root
B
y is equal to the fraction with numerator plus or minus square root of x and denominator 3 plus 2 thirds
C
y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 3
D
y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 9
14

Which graph represents the function f of x is equal to absolute value of x minus 4 ?

A
Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at 4 comma 0, ascends to the left passing through 0 comma 4, and ascends to the right passing through 5 comma 1.
B
Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at 0 comma negative 4, ascends to the left passing through negative 5 comma 1, and ascends to the right passing through 4 comma 0.
C
Image with description A coordinate plane with a V-shaped curve opening upward with its vertex at 0 comma negative 4. The curve passes through the point negative 4 comma 0 and the point 4 comma 0, with the left side rising at a slope of negative 1 and the right side rising at a slope of 1.
D
Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at negative 4 comma 0, ascends to the left passing through negative 6 comma 2, and ascends to the right passing through 0 comma 4.
15

Which graph represents the function p times x is equal to start absolute value x minus 1 end absolute value ?

A
Image with description A coordinate plane with a V-shaped graph formed by two rays. The x-axis is labeled from negative 6 to 6 in increments of 1 and the y-axis is labeled from negative 6 to 6 in increments of 1. The letter y labels the vertical axis at the top and the letter x labels the horizontal axis at the right. The vertex of the V-shape is at 1 comma 1. One ray extends from the vertex upward and to the left, ending with an arrow at approximately negative 5 comma 6. The other ray extends from the vertex upward and to the right, ending with an arrow at approximately 5 comma 5.
B
Image with description A coordinate plane with a V-shaped graph formed by two rays. The x-axis is labeled from negative 6 to 6 in increments of 1 and the y-axis is labeled from negative 6 to 6 in increments of 1. The letter y labels the vertical axis at the top and the letter x labels the horizontal axis at the right. The vertex of the V-shape is at negative 1 comma 0. One ray extends from the vertex upward and to the left, ending with an arrow at approximately negative 5 comma 4. The other ray extends from the vertex upward and to the right, ending with an arrow at approximately 4 comma 5.
C
Image with description A coordinate plane with a V-shaped graph formed by two rays. The x-axis is labeled from negative 6 to 6 in increments of 1 and the y-axis is labeled from negative 6 to 6 in increments of 1. The letter y labels the vertical axis at the top and the letter x labels the horizontal axis at the right. The vertex of the V-shape is at 0 comma 2. One ray extends from the vertex upward and to the left, ending with an arrow at approximately negative 5 comma 5. The other ray extends from the vertex upward and to the right, ending with an arrow at approximately 5 comma 6.
D
Image with description A coordinate plane with a V-shaped graph formed by two rays. The x-axis is labeled from negative 6 to 6 in increments of 1 and the y-axis is labeled from negative 6 to 6 in increments of 1. The letter y labels the vertical axis at the top and the letter x labels the horizontal axis at the right. The vertex of the V-shape is at 0 comma 1. One ray extends from the vertex upward and to the left, ending with an arrow at approximately negative 5 comma 6. The other ray extends from the vertex upward and to the right, ending with an arrow at approximately 5 comma 6.
16

Which could be the graph of f of x is equal to start absolute value x minus h end absolute value plus k if h and k are both positive?

A
Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at 1 comma negative 4 and y-intercept at 0 comma negative 3.
B
Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at negative 4 comma negative 5 and y-intercept at 0 comma negative 1.
C
Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at 2 comma 1.
D
Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at negative 3 comma 2 and y-intercept at 0 comma 5.
17

On each coordinate plane, the parent function f of x is equal to absolute value of x is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g of x is equal to start absolute value x plus 2 end absolute value as a solid line?

A
Image with description A coordinate plane with two V-shaped graphs. The horizontal axis and vertical axis are labeled from negative 6 to 6 in increments of 1. The first graph is a solid line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a dashed line, opens upward with its vertex at 1 comma 0, and passes through the points negative 1 comma 2 and 3 comma 2.
B
Image with description A coordinate plane with two V-shaped graphs. The horizontal axis and vertical axis are labeled from negative 6 to 6 in increments of 1. The first graph is a solid line labeled f of x equals absolute value of x, opens downward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma negative 1 and 1 comma negative 1. The second graph is a dashed line, opens downward with its vertex at 1 comma 0, and passes through the points negative 1 comma negative 2 and 3 comma negative 2.
C
Image with description " A coordinate plane with two V-shaped graphs. The horizontal axis and vertical axis are labeled from negative 6 to 6 in increments of 1. The first graph is a solid line labeled f of x equals absolute value of x, opens downward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma negative 1 and 1 comma negative 1. The second graph is a dashed line, opens downward with its vertex at 1 comma 0, and passes through the points negative 1 comma negative 2 and 3 comma negative 2."
D
Image with description A coordinate plane with two V-shaped curves. The x-axis is labeled from negative 6 to 6 and the y-axis is labeled from negative 6 to 6. A dashed V-shaped curve with its vertex at the origin 0 comma 0 opens upward with slopes of 1 and negative 1. A solid V-shaped curve with its vertex at 0 comma 2 opens upward with slopes of 1 and negative 1.
18

Consider the functions f of x is equal to 3 x squared , g of x is equal to 1 over 3 x , and h of x is equal to 3 x Which statements accurately compare the domain and range of the functions? Choose two correct answers.

A
The range of all three functions is all real numbers.
B
The range of f of x and h of x is all real numbers, but the range of g of x is all real numbers except 0 .
C
All of the functions have a unique range.
D
The domain of all three functions is all real numbers.
E
The domain of f of x and h of x is all real numbers, but the domain of g of x is all real numbers except 0 .
19

On each coordinate plane, the parent function f of x is equal to absolute value of x is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g of x is equal to absolute value of x minus 4 as a solid line?

A
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 0 comma negative 4, and passes through the points negative 4 comma 0 and 4 comma 0.
B
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 4 comma 0, and passes through the points 2 comma 2 and 6 comma 2.
C
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at negative 4 comma 0, and passes through the points negative 6 comma 2 and negative 2 comma 2.
D
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 0 comma 4, and passes through the points negative 2 comma 6 and 2 comma 6.
20

Which equation can be simplified to find the inverse of y is equal to 5 x squared plus 10 ?

A
y is equal to 1 fifth x squared plus 1 tenth
B
x is equal to 5 y squared plus 10
C
1 over y is equal to 5 x squared plus 10
D
negative y is equal to 5 x squared plus 10

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