AnswersCMS 2026-2027 NC Math 2 CREDIT RECOVERYTranslations of the Square Root Function

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1
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What is the range of the function f of x is equal to square root of x minus 8 plus 6 ?

A
f of x is greater than or equal to 8
B
f of x is greater than or equal to 6
C
f of x is greater than or equal to negative 8
D
f of x is greater than or equal to negative 6
2
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The function f of x is equal to square root of x is translated using the rule x comma y rightarrow x minus 6 comma y plus 9 to create cap A times x Which expression describes the range of cap A times x ?

A
y is greater than or equal to 6
B
y is greater than or equal to negative 9
C
y is greater than or equal to 9
D
y is greater than or equal to negative 6
3

Which graph represents the function f of x is equal to square root of x minus 2 ?

A
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from 0 comma 2, moves right and passes through the point 4 comma 4.
B
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from negative 2 comma 0, moves right and passes through the point 2 comma 2.
C
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from 2 comma 0, moves right and passes through the point 3 comma 1.
D
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from 0 comma negative 2, moves right and passes through the point 4 comma 0.
4

The function f of x is equal to square root of x is translated left 5 units and up 3 units to create the function g of x What is the domain of g of x ?

A
start set x such that x is greater than or equal to negative 3 end set
B
start set x such that x is greater than or equal to 5 end set
C
start set x such that x is greater than or equal to 3 end set
D
start set x such that x is greater than or equal to negative 5 end set
5

A function h of x is defined by the equation h of x is equal to square root of x minus 2 end root plus 3 Which is the graph of h of x ?

A
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from negative 2 comma 3, moves right and passes through the point 6 comma 6.
B
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from negative 2 comma negative 3, moves right and passes through the point 6 comma 0.
C
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from 2 comma 3, moves right and passes through the point 10 comma 6.
D
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from 2 comma negative 3, moves right and passes through the point 10 comma 0.
6

Which graph represents the function f of x is equal to square root of x plus 3 ?

A
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1 is given. A smooth curve originates from the point 0 comma 3, goes to the right and passes through the points 1 comma 4 and 4 comma 5.
B
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1 is given. A smooth curve originates from the point 0 comma negative 3, goes to the right and passes through the point 4 comma negative 1.
C
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1 is given. A smooth curve originates from the point negative 3 comma 3, goes to the right and passes through the point 1 comma 5.
D
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1 is given. A smooth curve originates from the point negative 3 comma 0 and goes to the right. It passes through the point 1 comma 2.
7

The graph of y is equal to square root of x is translated. The translation is defined by x plus 1 comma y minus 2 Which is the graph of the translated image?

A
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from the point 1 comma negative 2, moves right and passes through the point 5 comma 0.
B
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from the point negative 2 comma 1, moves right and passes through the point 2 comma 3.
C
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from the point 2 comma 2, moves right and passes through the point 3 comma 3.
D
Image with description A coordinate plane with x and y axes ranges from negative 5 to 5 in increments of 1. A smooth curve originates from the point negative 1 comma negative 2, moves right and passes through the point 3 comma 0.
8

The graph of f of x is equal to square root of x is translated to create g of x so that the domain remains the same but the range of g of x is all real numbers greater than or equal to 8 Which graph represents g of x ?

A
Image with description A coordinate plane with x and y axes ranges from negative 20 to 20 in increments of 4. A smooth curve originates from origin, moves right and passes through the point 12 comma 4.
B
Image with description A coordinate plane with x and y axes ranges from negative 20 to 20 in increments of 4. A smooth curve originates from the point negative 8 comma 0, moves right and passes through the point 8 comma 4.
C
Image with description A coordinate plane with x and y axes ranges from negative 20 to 20 in increments of 4. A smooth curve originates from the point 8 comma 0, moves right and passes through the point 20 comma 4.
D
Image with description A coordinate plane with x and y axes ranges from negative 20 to 20 in increments of 4. A smooth curve originates from origin, moves right and passes through the point 12 comma 4.
9

Which function has a domain of start set x such that x is greater than or equal to 8 end set ?

A
f of x is equal to square root of x plus 1 end root minus 8
B
f of x is equal to square root of x plus 8 end root minus 1
C
f of x is equal to square root of x minus 8 end root plus 1
D
f of x is equal to square root of x minus 1 end root plus 8
10

The graph of y is equal to square root of x is translated so that the domain of the new function is start set x such that x is greater than or equal to negative 6 end set and the range is start set y such that y is greater than or equal to 0 end set Which graph represents the translated image?

A
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from the point 0 comma negative 6, moves right and passes through the point 4 comma negative 4.
B
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from the point negative 6 comma 0, moves right and has y-intercept.
C
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from the point negative 6 comma 6, moves right and has y-intercept. It also passes through the point 10 comma 10.
D
Image with description A coordinate plane with x and y axes ranges from negative 10 to 10 in increments of 2. A smooth curve originates from the point negative 6 comma negative 6, moves right and has y-intercept. It also passes through the point 10 comma negative 2.

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