5.3 Graphing Radical Functions

Front

What is a radical function?

Back

A function that includes a variable within a radical (square root, cube root, etc.).

Front

What is the parent function of a square root function?

Back

f(x) = √x.

Front

What is the domain of the square root function f(x) = √x?

Back

x ≥ 0.

Front

What is the range of the square root function f(x) = √x?

Back

y ≥ 0.

Front

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

Back

The output values (y-values) are negated.

Front

What does a vertical stretch by a factor of 5 do to the function f(x)?

Back

It multiplies the output values by 5, making the graph taller.

Front

What is the effect of a vertical shrink by a factor of 1/5 on the function f(x)?

Back

It multiplies the output values by 1/5, making the graph shorter.

Front

How do you determine the range of a radical function?

Back

Analyze the output values (y-values) based on the transformations applied to the parent function.

Front

What is the range of the function g(x) = -√x?

Back

y ≤ 0.

Front

What is the effect of a reflection over the y-axis on the function f(x)?

Back

The input values (x-values) are negated.