Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does shifting a function left or right mean?

Back

Shifting a function left or right involves adding or subtracting a value from the input variable (x). For example, f(x) + c shifts the graph left by c units, while f(x - c) shifts it right by c units.

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. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

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. If f(x) is the original function, the reflected function is -f(x).

Front

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

Back

Reflecting a function over the y-axis changes the sign of the input values. If f(x) is the original function, the reflected function is f(-x).

Front

What does it mean to stretch or compress a function vertically?

Back

A vertical stretch occurs when the output values are multiplied by a factor greater than 1, making the graph taller. A vertical compression occurs when the output values are multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does it mean to stretch or compress a function horizontally?

Back

A horizontal stretch occurs when the input values are multiplied by a factor less than 1, making the graph wider. A horizontal compression occurs when the input values are multiplied by a factor greater than 1, making the graph narrower.

Front

How do you shift the function f(x) = x^3 three units left?

Back

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

Front

What is the transformation for g(x) if f(x) = x^3 and g(x) is shifted down by 1 unit?

Back

The transformation is represented as g(x) = x^3 - 1.

Front

If f(x) = √x, what is the transformation for g(x) if it is reflected over the x-axis?

Back

The transformation is represented as g(x) = -√x.