Graphing Square and Cube Root Functions

Front

What is the domain of a cube root function?

Back

All real numbers (x = All real numbers)

Front

What is the range of a cube root function?

Back

All real numbers (y = All real numbers)

Front

What type of function is represented by the graph of f(x) = ∛(x)?

Back

Cubic Root Function

Front

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

Back

x ≥ 0

Front

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

Back

y ≥ 0

Front

What transformation occurs when the graph of f(x) = √(x) is stretched vertically by a factor of 2?

Back

The graph becomes steeper, stretching away from the x-axis.

Front

What does it mean to reflect a function over the x-axis?

Back

The y-values of the function are multiplied by -1.

Front

If f(x) = ∛(x) is reflected over the x-axis, what is the new function?

Back

f(x) = -∛(x)

Front

What is the effect of shifting a function left by 9 units?

Back

The function f(x) becomes f(x + 9).

Front

If f(x) = ∛(x) is vertically shrunk by a factor of 1/4, what is the new function?

Back

f(x) = (1/4)∛(x)