Transformations of Functions PRECALCULUS

Front

What is an even function?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain of f. Graphically, even functions are symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f. Graphically, odd functions are symmetric about the origin.

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 of a function, moving the graph left or right without changing its shape.

Front

What does it mean to stretch a function vertically?

Back

Stretching a function vertically means multiplying the function by a factor greater than 1, which makes the graph taller.

Front

What does it mean to compress a function vertically?

Back

Compressing a function vertically means multiplying the function by a factor between 0 and 1, which makes the graph shorter.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means multiplying the function by -1, which flips the graph upside down.

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means replacing x with -x in the function, which flips the graph horizontally.

Front

How do you identify a vertical shift in the function y = x^2 + 2?

Back

The '+2' indicates a vertical shift up by 2 units from the parent function y = x^2.

Front

How do you identify a horizontal shift in the function y = (x - 3)^2?

Back

The '(x - 3)' indicates a horizontal shift to the right by 3 units from the parent function y = x^2.