transformation of parent functions 11G1

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which can be transformed to create other functions in that family.

Front

What does it mean to compress a function vertically?

Back

To compress a function vertically means to multiply the function by a factor between 0 and 1, which makes the graph closer to the x-axis.

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch occurs when a function is multiplied by a factor greater than 1, making the graph taller and further from the x-axis.

Front

How does a horizontal translation affect a function?

Back

A horizontal translation shifts the graph left or right along the x-axis, depending on the sign of the value added or subtracted from x.

Front

What is the transformation for f(x) = x shifted left 3 units?

Back

The transformation is f(x) = (x + 3).

Front

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

Back

Reflecting a function over the x-axis means to multiply the function by -1, flipping the graph upside down.

Front

What is the transformation for f(x) = x^2 reflected over the x-axis and shifted up 4?

Back

The transformation is f(x) = -x^2 + 4.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function results in a vertical translation of the graph; if the constant is positive, the graph shifts up, and if negative, it shifts down.

Front

How do you translate a function right 2 units?

Back

To translate a function right 2 units, replace x with (x - 2) in the function.

Front

What is the transformation for f(x) = x^2 translated left 4 units?

Back

The transformation is f(x) = (x + 4)^2.