U-3:Lesson 2 Graphing Radical Functions

Front

What is a radical function?

Back

A function that involves a root, such as a square root or cube root, typically expressed in the form f(x) = √(x) or f(x) = ∛(x).

Front

What is the parent function of a square root function?

Back

f(x) = √(x), which is defined for x ≥ 0 and has a range of y ≥ 0.

Front

What is the parent function of a cube root function?

Back

f(x) = ∛(x), which is defined for all real numbers and has a range of all real numbers.

Front

How does shifting a graph to the right affect its equation?

Back

To shift a graph to the right by 'h' units, replace x with (x - h) in the function's equation.

Front

How does shifting a graph upward affect its equation?

Back

To shift a graph upward by 'k' units, add 'k' to the function's equation.

Front

What does reflecting a graph over the x-axis do to its equation?

Back

To reflect a graph over the x-axis, multiply the entire function by -1.

Front

What does reflecting a graph over the y-axis do to its equation?

Back

To reflect a graph over the y-axis, replace x with -x in the function's equation.

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch by a factor of 'a' (where a > 1) multiplies the function's output by 'a', making the graph taller.

Front

What is the effect of a vertical shrink on a function?

Back

A vertical shrink by a factor of 'b' (where 0 < b < 1) multiplies the function's output by 'b', making the graph shorter.

Front

What is the range of the function f(x) = √(x - 2) + 3?

Back

The range is y ≥ 3, since the minimum value occurs when x = 2.