5.3 & 5.4 Radical Functions & Equations Review GHS

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is f(x) = √(x) or f(x) = n√(x).

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the function is defined. For even roots, the expression under the radical must be non-negative.

Front

What is the range of a radical function?

Back

The range of a radical function is the set of all possible output values (f(x)). For square root functions, the range is typically [0, ∞).

Front

How do you solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side, square both sides to eliminate the radical, and then solve the resulting equation.

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down on the coordinate plane. Adding a constant to the function shifts it up, while subtracting shifts it down.

Front

What does it mean to shift a graph horizontally?

Back

Shifting a graph horizontally means moving it left or right. Adding a constant inside the function shifts it left, while subtracting shifts it right.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a reflection over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a reflection over the y-axis?

Back

A reflection over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

What is the effect of a negative sign in front of a radical function?

Back

A negative sign in front of a radical function reflects the graph over the x-axis.