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Example Questions
Example Question #1 : Understanding Polynomial Functions
It took Jack 25 minutes to travel 14 miles, what was Jack's average speed in mph?
* We have to change the time from minutes to hours, there are 60 minutes in one hour.
Example Question #2 : Understanding Polynomial Functions
Let and
. Evaluate
.
Substitute into
, and then substitute the answer into
.
Example Question #2 : Understanding Polynomial Functions
Solve the following system of equations:
Infinite solutions.
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 #1 : Transformations Of Polynomial Functions
List the transformations that have been enacted upon the following equation:
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 stretch by a factor of 4
horizontal compression by a factor of 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 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
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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