M2L6 TRANSFORMATIONS

Parent functions are the most basic form of a function. They are centered or oriented around the origin (0,0).

See some of our most common parent functionsbelow:1. Linear 2. Quadratic 3. Cubic 4. Radical 5. Absolute value 6. Exponential 7. Rational

Putting numbers into the parent function transforms it into something new. The letters a, h, & k are used to represent where we place numbers.

1. Linear 2. Quadratic 3. Cubic 4. Radical 5. Absolute value 6. Exponential 7. Rational or

First, let’s look at what the a can do to a function.

If |a|>1, then it vertically stretches the function (looks taller & skinnier)

If 0<|a|<1, then it vertically shrinks the function(looks shorter and fatter)

-a reflects the function over the x axis.

Next, let’s look at what the h can do to a function.

If you have (x-h), the function is shifted right h units

If you have (x+h), the function is shifted left h units

Next, let’s look at what the k can do to a function.

If you have (x)-k, the function is shifted down k units

If you have (x)+k, the function is shifted up k units

A less common transformation is reflecting the function over the y axis (mirror image).To create a y axis reflection, you negate the x inside of it’s grouping symbols.

For example: OR OR

Two more less common transformations arehorizontal stretching and horizontal shrinking.

To create a horizontal change, you place a number in front of x inside of it’s grouping symbols.

For example: or or

Specifics on horizontal stretching and horizontal shrinking:

• If the coefficient is >1, then it horizontally shrinks the function

• If the coefficient is between 0 and 1, then it horizontally stretches the function.

All of those transformation rules work on any of our functions!

Let’s try an example. Given , shift it up 10 and left 7, reflect it across the x axis, and vertically stretch it by 5.

• now it’s shifted up 10• now we’ve added the shift left 7• now we’ve reflected it over the x axis• lastly, we vertically stretched it by 5

What if it already has transformations and we’re asked to change it?Let’s try that. Given , shift it up 4 and reflect it across the y axis.

• this shifts it up 4, but we should combine like terms• now we just need to negate the x• It’s done.

Here are some extra resources to help you:Group of video tutorials:• https://

www.tes.com/lessons/x0Ei03pVKLMCxg/m2l6-transformations-of-functions

Website with graph examples:• http://

www.regentsprep.org/regents/math/algtrig/atp9/funclesson1.htm

• https://www.mathsisfun.com/sets/function-transformations.html