Vertical Stretches and Shrinks of the Square Root Function — Quiz

Question 3 • Algebra 2 with Probability

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

Answer

Image with description A coordinate plane with x-axis labeled from negative 2 to 8 in increments of 1, y-axis labeled from negative 7 to 3 in increments of 1. A curve originates from origin and passes through the points 1 comma negative 3 and 4 comma negative 6 in the fourth quadrant.

Image with description A coordinate plane with x-axis labeled from negative 3 to 7 in increments of 1, y-axis labeled from negative 1 point 5 to 3 point 5 in increments of 0 point 5. A smooth curve originates from origin and passes through the points 1 comma 0 point 3 and 4 comma 0 point 6.

Image with description A coordinate plane with x-axis labeled from negative 2 to 8 in increments of 1, y-axis labeled from negative 3 point 5 to 3 in increments of 0 point 5. A curve originates from origin and passes through the points 1 comma negative 0 point 3 and 4 comma negative 0 point 6.

Image with description A coordinate plane with x-axis labeled from negative 3 to 7 in increments of 1, y-axis labeled from negative 3 to 7 in increments of 1. A smooth curve originates from origin and passes through the points 1 comma 3 and 4 comma 6.

Explanation

For f(x) = 3√x, multiply the square root of x by 3. For example, f(1) = 3√1 = 3 and f(4) = 3√4 = 6, so the graph passes through (1, 3) and (4, 6). Choice D shows those points and starts at the origin.

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