Vertical Stretches and Shrinks of the Square Root Function — Quiz

Question 10 • Algebra 2 with Probability

Which is the graph of f of x is equal to 1 half square root of x ?

Answer

Image with description A coordinate plane with a curve. 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. A curve starts at the origin point 0 comma 0 and curves upward and to the right in the first quadrant, passing through the points 1 comma 2 and 4 comma 4.

Image with description A coordinate plane with a curve. 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. A curve starts at the origin point 0 comma 0 and curves gently upward and to the right in the first quadrant, passing through the point 4 comma 1.

Image with description A coordinate plane with a curve. 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. A curve starts at the origin point 0 comma 0 and curves downward and to the right in the fourth quadrant, passing through the points 1 comma negative 2 and 4 comma negative 4.

Image with description A coordinate plane with a curve. 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. A curve starts at the origin point 0 comma 0 and curves gently downward and to the right in the fourth quadrant, passing through the point 4 comma negative 1.

Explanation

The function is f(x) = (1/2)√x, so its graph starts at (0, 0) and rises to the right. For example, when x = 4, f(4) = (1/2)√4 = 1, matching the graph that passes through (4, 1): choice B.

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