Transformations of Functions — Quiz

Question 13 • Mathematics III

Which graph is an example of a function whose parent function is y is equal to square root of x ?

Answer

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The curve starts at (negative 4 comma negative 1), passes through (negative 3 comma 0) and then curves up and increases to the right into quadrant 1.

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. 2 curves are drawn. Both curves have an asymptote at x equals negative 1. One curve decreases from quadrant 2 into quadrant 1 and approaches y equals 1. It crosses the y-axis at (0 comma 2). The other curve approaches y equals 1 in quadrant 1 and then curves down and approaches y equals negative 1 in quadrant 3. It crosses the x axis at (negative 2, 0).

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The curve starts in quadrant 3 and then increases into quadrant 1. It crosses y axis at (0 comma negative 2) and crosses the x axis at (1 point 5 comma 0).

Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The parabola opens upwards, has a vertex at (0 comma 1).

Explanation

The parent function y = √x begins at (0, 0), is defined from that point to the right, and curves upward while becoming less steep. Choice D has the same square-root shape, shifted 4 units left and 1 unit down: it begins at (−4, −1) and passes through (−3, 0).

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