Graphing Square and Cube Root Functions

Front

What is the parent function of a square root function?

Back

f(x) = √x

Front

What transformation occurs when a function is reflected over the x-axis?

Back

The output values (y-values) are multiplied by -1.

Front

How does a vertical stretch by a factor of k affect the graph of a function?

Back

It makes the graph taller by a factor of k.

Front

What is the effect of a vertical shrink by a factor of k on a function?

Back

It compresses the graph towards the x-axis by a factor of k.

Front

What is the general form of a cube root function?

Back

f(x) = ∛x

Front

How do you shift a graph to the right by h units?

Back

Replace x with (x - h) in the function.

Front

What is the effect of subtracting a constant from a function?

Back

It shifts the graph down by that constant.

Front

What is the equation of a square root function that has been shifted right 3 units and down 2 units?

Back

f(x) = √(x - 3) - 2

Front

What type of function is represented by the equation y = ∛(x + 1)?

Back

Cubic Root Function

Front

How do you identify a square root function from its graph?

Back

It has a starting point and increases gradually, resembling half of a sideways parabola.