Functions Transformations

Front

What is a vertical stretch in function transformations?

Back

A vertical stretch occurs when a function is multiplied by a factor greater than 1, making the graph taller.

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means adding a positive value to the input variable (x) in the function.

Front

How does the transformation y = f(x) + k affect the graph?

Back

The graph of y = f(x) is shifted vertically by k units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

What is the effect of replacing f(x) with f(x - h)?

Back

This transformation shifts the graph of f(x) horizontally to the right by h units.

Front

What does the transformation y = -f(x) represent?

Back

This transformation reflects the graph of f(x) across the x-axis.

Front

How do you represent a leftward shift in a function?

Back

A leftward shift is represented by f(x + h), where h is a positive value.

Front

What is the transformation of f(x) = x^2 to g(x) = (x - 3)^2 + 1?

Back

This represents a shift of the graph 3 units to the right and 1 unit up.

Front

What happens to the graph of f(x) when you apply f(x) - k?

Back

The graph shifts down by k units.

Front

What is the transformation of f(x) = x^3 to g(x) = x^3 + 4?

Back

This transformation shifts the graph of f(x) up by 4 units.

Front

How does the transformation f(x) = 2f(x) affect the graph?

Back

This transformation vertically stretches the graph by a factor of 2.