AnswersAlgebra 2 with ProbabilityTranslations of the Square Root Function — QuizQuestion 1
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Translations of the Square Root Function — Quiz

Question 1 • Algebra 2 with Probability

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?

Answer
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.

Explanation

The graph of y = √x begins at (0, 0). To make the domain x ≥ −6, shift it 6 units left; keeping the range y ≥ 0 means there is no vertical shift. The translated graph begins at (−6, 0), and at x = −2 it has y = √(−2 + 6) = 2. Choice A has these features.

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