Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the position, size, or shape of its graph.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does a vertical stretch affect the graph of a function?

Back

A vertical stretch makes the graph taller and narrower, multiplying the output values by a factor greater than 1.

Front

What does shifting a function to the right mean?

Back

Shifting a function to the right means adding a positive value to the input (x) in the function's equation.

Front

What is the effect of reflecting a function over the x-axis?

Back

Reflecting a function over the x-axis changes the sign of the output values, resulting in a vertical flip of the graph.

Front

How do you represent a vertical shift of a function?

Back

A vertical shift is represented by adding or subtracting a constant from the function's output (f(x) ± k).

Front

What is the transformation for f(x) = x^2 shifted down 3 units?

Back

The transformation is represented as f(x) = x^2 - 3.

Front

What does the equation g(x) = (x - 2)^2 represent?

Back

This equation represents a horizontal shift of the parent function f(x) = x^2 to the right by 2 units.

Front

What is the transformation for f(x) = x^3 shifted left 4 units?

Back

The transformation is represented as f(x) = (x + 4)^3.

Front

What does a negative sign in front of a function indicate?

Back

A negative sign indicates a reflection over the x-axis.