Polynomial Functions - Math

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.

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

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

Substitute into , and then substitute the answer into .

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.

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

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

Substitute into , and then substitute the answer into .

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.

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

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

Substitute into , and then substitute the answer into .

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.

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

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

Substitute into , and then substitute the answer into .