Transformations of Functions

Front

What is a vertical stretch of a function?

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

What happens to the graph of f(x) when it is replaced with 2⋅f(x)?

Back

The graph undergoes a vertical stretch by a factor of 2.

Front

What is a horizontal translation of a function?

Back

A horizontal translation shifts the graph left or right without changing its shape.

Front

How does g(x) = (x + 4)² transform f(x) = x²?

Back

It translates the graph of f(x) 4 units to the left.

Front

What is the effect of changing f(x) to f(x - h)?

Back

This represents a horizontal translation to the right by h units.

Front

What does it mean for a function to be narrower than its parent function?

Back

A function is narrower if it grows faster than the parent function, typically due to a vertical stretch.

Front

How does y = 5x² compare to y = x²?

Back

y = 5x² is narrower than y = x² due to the vertical stretch by a factor of 5.

Front

What is a vertical compression of a function?

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

What transformation is represented by g(x) = x² - 5?

Back

This represents a vertical translation down by 5 units.

Front

What does g(x) = -f(x) indicate about the graph of f(x)?

Back

It indicates a reflection across the x-axis.