# High School Math : Transformations of Polynomial Functions

## Example Questions

### Example Question #1 : Transformations Of Polynomial Functions

List the transformations that have been enacted upon the following equation:

vertical stretch by a factor of 4

horizontal stretch by a factor of 6

vertical translation 7 units down

horizontal translation 3 units right

vertical stretch by a factor of 4

horizontal compression by a factor of 6

vertical translation 7 units down

horizontal translation 3 units left

vertical stretch by a factor of 4

horizontal compression by a factor of 6

vertical translation 7 units down

horizontal translation 3 units right

vertical stretch by a factor of 1/4

horizontal compression by a factor of 1/6

vertical translation 7 units down

horizontal translation 3 units right

vertical compression by a factor of 4

horizontal stretch by a factor of 6

vertical translation 7 units down

horizontal translation 3 units right

vertical stretch by a factor of 4

horizontal compression by a factor of 6

vertical translation 7 units down

horizontal translation 3 units right

Explanation:

Since the equation given in the question is based off of the parent function , we can write the general form for transformations like this:

determines the vertical stretch or compression factor.

• If is greater than 1, the function has been vertically stretched (expanded) by a factor of .
• If is between 0 and 1, the function has been vertically compressed by a factor of .

In this case, is 4, so the function has been vertically stretched by a factor of 4.

determines the horizontal stretch or compression factor.

• If  is greater than 1, the function has been horizontally compressed by a factor of .
• If  is between 0 and 1, the function has been horizontally stretched (expanded) by a factor of .

In this case,  is 6, so the function has been horizontally compressed by a factor of 6. (Remember that horizontal stretch and compression are opposite of vertical stretch and compression!)

determines the horizontal translation.

• If is positive, the function was translated units right.
• If is negative, the function was translated units left.

In this case, is 3, so the function was translated 3 units right.

determines the vertical translation.

• If  is positive, the function was translated  units up.
• If  is negative, the function was translated  units down.

In this case,  is -7, so the function was translated 7 units down.