Translations of the Square Root Function — Quiz

Question 7 • Algebra 2 with Probability

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 ?

Answer

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.

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.

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.

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.

Explanation

The function is h(x) = √(x − 2) + 3. The square-root graph is shifted 2 units right and 3 units up, so it begins at (2, 3). For example, h(6) = √(6 − 2) + 3 = 5, matching the graph that passes through (6, 5). That is choice A.

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