1-2 Transformations of Functions

Front

What is a vertical shift in function transformations?

Back

A vertical shift moves the graph of a function up or down without changing its shape.

Front

How does the equation g(x) = f(x) + k affect the graph of f(x)?

Back

It shifts the graph of f(x) vertically by k units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

What is a horizontal shift in function transformations?

Back

A horizontal shift moves the graph of a function left or right without changing its shape.

Front

How does the equation g(x) = f(x - h) affect the graph of f(x)?

Back

It shifts the graph of f(x) horizontally by h units; if h is positive, it shifts right, and if h is negative, it shifts left.

Front

What does a vertical stretch of a function 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.

Front

How does the equation g(x) = af(x) affect the graph of f(x) when a > 1?

Back

It vertically stretches the graph of f(x) by a factor of a.

Front

What does a vertical compression of a function 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.

Front

How does the equation g(x) = af(x) affect the graph of f(x) when 0 < a < 1?

Back

It vertically compresses the graph of f(x) by a factor of a.

Front

What does reflection over the x-axis mean in function transformations?

Back

Reflection over the x-axis flips the graph of the function upside down.

Front

How does the equation g(x) = -f(x) affect the graph of f(x)?

Back

It reflects the graph of f(x) over the x-axis.