Translations of the Square Root Function — Quiz

Question 3 • Algebra 2 with Probability

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

Answer

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.

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.

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.

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.

Explanation

For f(x) = √x + 3, the square-root graph is shifted up 3 units. It starts at (0, 3), then rises while gradually flattening, which matches the graph described in choice D. Choice A instead starts around x = −3, suggesting a horizontal shift.

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