Function Transformations

Front

What is a function transformation?

Back

A function transformation refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

Tags

CCSS.HSF.BF.B.3

Front

What does a vertical shift of a function mean?

Back

A vertical shift moves the graph of a function up or down. For example, if f(x) is shifted up by 3, the new function is f(x) + 3.

Front

What does a horizontal shift of a function mean?

Back

A horizontal shift moves the graph of a function left or right. For example, if f(x) is shifted left by 2, the new function is f(x + 2).

Front

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

Back

A negative sign in front of a function reflects the graph across the x-axis. For example, if f(x) is reflected, the new function is -f(x).

Front

What does a vertical stretch mean?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, f(x) becomes 2f(x).

Front

What does a vertical compression mean?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, f(x) becomes 0.5f(x).

Front

What does a horizontal stretch mean?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider. For example, f(x) becomes f(0.5x).

Front

What does a horizontal compression mean?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor between 0 and 1, making the graph narrower. For example, f(x) becomes f(2x).

Front

Back

In this equation, h represents a horizontal shift (right if h > 0, left if h < 0) and k represents a vertical shift (up if k > 0, down if k < 0).

Front

Back

The equation represents a reflection of the graph of f(x) across the x-axis.

Tags

CCSS.HSF.BF.B.3