High School Math : Polynomial Functions

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Polynomial Functions

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

Possible Answers:

Correct answer:

Explanation:

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

 

Example Question #2 : Polynomial Functions

Let and .  Evaluate .

Possible Answers:

Correct answer:

Explanation:

Substitute into , and then substitute the answer into .

 

 

Example Question #3 : Polynomial Functions

Solve the following system of equations:

Possible Answers:

Infinite solutions.

Correct answer:

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 #4 : Polynomial Functions

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

Possible Answers:

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

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 1/4

horizontal compression by a factor of 1/6

vertical translation 7 units down

horizontal translation 3 units right

Correct answer:

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.

 

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