Question

The graph of y =$\sqrt[]{x}$nis transformed as shown in the graph below. Which equation represents the transformed function?

Answer 1

Answer:

$\textsf{A)}\quad y=-\sqrt{x}+2$

Step-by-step explanation:

Parent function:

$y = \sqrt{x}$

The properties of the parent function are:

• Starts at the origin, so y-intercept is at (0, 0)
• Domain: x ≥ 0
• Range: y ≥ 0
• As x increases, y increases

From inspection of the graph, as the x-values increase, the y-values decrease. Therefore there has been a reflection in the x-axis.

The y-intercept is now at (0, 2), therefore the function has been translated 2 units up.

Translations

For a > 0

$y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

Therefore:

Reflected in the x-axis:  $-f(x)=-\sqrt{x}$

Then translated 2 units up:  $-f(x)+2=-\sqrt{x}+2$

So the equation that represents the transformed function is:

$y=-\sqrt{x}+2$