Question

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

Answer 1

`\textsf{A)}\quad y=-√(x)+2`

Explanation:

Parent function:

`y = √(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)=-√(x)`

Then translated 2 units up:
`-f(x)+2=-√(x)+2`

So the equation that represents the transformed function is:

`y=-√(x)+2`