AnswersAlgebra 2 with ProbabilityTranslations of the Square Root Function

Translations of the Square Root Function — Quiz Answers

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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 a square root function. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A curve starts at the point negative 6 comma 0 on the negative x-axis and curves towards the first quadrant, passing through the point negative 2 comma 2 and extending to the point 10 comma 4.
B
Image with description A coordinate plane with a square root function. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A curve starts at the point negative 6 comma 6 and curves towards the first quadrant, passing through the point negative 2 comma 8 and extending to the point 10 comma 10.
C
Image with description A coordinate plane with a square root function. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A curve starts at the point 0 comma negative 6 on the negative y-axis and curves progressively in the fourth quadrant, passing through the point 4 comma negative 4 and extending to the point 10 comma negative 2 point 7.
D
Image with description A coordinate plane with a square root function. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A curve starts at the point negative 6 comma negative 6 and curves upwards and to the fourth quadrant, passing through the point negative 2 comma negative 4 and extending to the point 10 comma negative 2.
2
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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 labeled 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.
B
Image with description A coordinate plane with x and y axes labeled 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.
C
Image with description A coordinate plane with x and y axes labeled 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.
D
Image with description A coordinate plane with x and y axes labeled 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.
3

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 a curve with a positive but decreasing slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve begins at the left side of the plane near negative 3 comma 1, rises steeply at first, then flattens as it extends to the right, ending near 3 comma 3.
B
Image with description A coordinate plane with a curve with a negative and decreasing slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve begins at the left side of the plane near negative 3 comma 5, descends steeply at first from left to right, then flattens as it extends toward the right, ending near 1 comma 4.
C
Image with description A coordinate plane with a curve with a positive and increasing slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve begins at the lower portion of the plane near 0 comma negative 4, rises with an increasing slope from left to right, and ends near 4 comma negative 1.
D
Image with description A coordinate plane with a curve with a positive but decreasing slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve begins near 0 comma 3, rises steeply at first, then flattens as it extends to the right, ending near 4 comma 4.
4

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 a curve. The x-axis is labeled from negative 20 to 20 in increments of 4 and the y-axis is labeled from negative 20 to 20 in increments of 4. A curve with a gradual increasing trend begins near the point negative 12 comma 0 on the x-axis in the second quadrant, rises slowly and continues to the right, passing through approximately the point 0 comma 4 on the y-axis and reaching approximately the point 16 comma 8, indicating a concave-down increasing curve spanning the second and first quadrants.
B
Image with description A coordinate plane with two straight lines and two shaded regions. The x-axis and y-axis are each labeled from negative 5 to 5 in increments of 1. A solid straight line with a positive slope passes through the origin and extends from approximately the point negative 3 comma negative 3 to the point 3 comma 3, with an arrow at each end. A dashed straight line with a steeper positive slope also passes near the origin and extends from approximately the point negative 2 comma negative 5 to the point 2 comma 5, with an arrow at each end. The region above the solid line and to the left is shaded, and the region below the dashed line and to the right is shaded, with the two shaded regions partially overlapping near the origin.
C
Image with description A coordinate plane with a curve. The x-axis is labeled from negative 20 to 20 in increments of 4 and the y-axis is labeled from negative 20 to 20 in increments of 4. A curve with a gradual increasing trend begins near the point 8 comma 0 on the x-axis, rises slowly as it moves to the right, reaching approximately the point 20 comma 4, indicating a concave-down increasing curve in the first quadrant with the curve starting just above the x-axis.
D
Image with description A coordinate plane with a curve. The x-axis is labeled from negative 20 to 20 in increments of 4 and the y-axis is labeled from negative 20 to 20 in increments of 4. A curve with a gradual increasing trend begins near the point 8 comma 0 on the x-axis, rises slowly as it moves to the right, reaching approximately the point 20 comma 4, indicating a concave-down increasing curve in the first quadrant with the curve starting just above the x-axis.
5

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 negative 8
B
f of x is greater than or equal to 6
C
f of x is greater than or equal to 8
D
f of x is greater than or equal to negative 6
6

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 minus 8 end root plus 1
B
f of x is equal to square root of x plus 1 end root minus 8
C
f of x is equal to square root of x plus 8 end root minus 1
D
f of x is equal to square root of x minus 1 end root plus 8
7

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 a square root curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. The curve begins at the point 2 comma 3, increases gradually to the right, and passes through the point 6 comma 5. The curve continues rising slowly as it extends to the right.
B
Image with description A coordinate plane with a square root curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. The curve begins at approximately x equals 2 on the x-axis, then gradually rises as it extends to the right, depicting a square root function shifted from the origin.
C
Image with description A coordinate plane with a square root curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. The curve begins at the point 2 comma negative 3 and moves upward and to the right, gradually leveling off as it extends across the graph.
D
Image with description A coordinate plane with a square root curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. The curve begins at the point negative 2 comma negative 3 and moves upward and to the right, gradually leveling off as it continues across the graph.
8

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
9

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 both the x and y-axes labeled from negative 5 to 5 in increments of 1. A curve originates from negative 2 comma 0, and increases to the right passing through the point 3 comma 1.
B
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A curve starts at the point 0 comma 2 and extends to the right. It passes through approximately the points 1 comma 2.8, 3 comma 3.7, and 5 comma 4.3.
C
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A curve starts at the point 1 comma negative 2 and extends to the right. It passes through approximately the points 2 comma negative 1, 3 comma negative 0.6, and 5 comma 0.2.
D
Image with description A coordinate plane with both the x and y-axes labeled from negative 5 to 5 in increments of 1. A curve originates from negative 2 comma 0, and increases to the right passing the y-axis between 1 and 2 and also through the point 2 comma 2.
10

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

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