Transformations Flashcard

Front

What is a vertical shift in a function?

Back

A vertical shift occurs when a constant is added to or subtracted from a function, moving the graph up or down without changing its shape.

Front

What is a horizontal shift in a function?

Back

A horizontal shift occurs when a constant is added to or subtracted from the input variable (x), moving the graph left or right.

Front

Back

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

Front

What does it mean to vertically stretch a function?

Back

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

Front

What does it mean to vertically compress a function?

Back

A vertical compression occurs when the output of the function is multiplied by a factor between 0 and 1, making the graph shorter and less steep.

Front

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

Back

A negative sign reflects the graph of the function across the x-axis.

Front

How do you identify a downward shift in a function's graph?

Back

A downward shift is identified when a constant is subtracted from the function, resulting in the entire graph moving down.

Front

Back

This equation represents a vertical stretch by a factor of 3 and a horizontal shift to the right by 4 units.

Front

Back

This equation indicates a horizontal shift to the left by 5 units and a vertical shift down by 2 units.

Front

How can you determine if a graph is steeper or less steep?

Back

A graph is steeper if the coefficient of the squared term is greater than 1, and less steep if it is between 0 and 1.