# High School Math : Polynomial Functions

## Example Questions

### Example Question #33 : Functions And Graphs

It took Jack 25 minutes to travel 14 miles, what was Jack's average speed in mph?

Explanation:

* We have to change the time from minutes to hours, there are 60 minutes in one hour.

### Example Question #34 : Functions And Graphs

Let and .  Evaluate .

Explanation:

Substitute into , and then substitute the answer into .

### Example Question #35 : Functions And Graphs

Solve the following system of equations:

Infinite solutions.

Explanation:

We will solve this system of equations by Elimination.  Multiply both sides of the first equation by 2, to get:

Then add this new equation, to the second original equation, to get:

or

Plugging this value of  back into the first original equation, gives:

or

### Example Question #36 : Functions And Graphs

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 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 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

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.