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Example Questions
Example Question #1 :Transformations Of Polynomial Functions
What transformations have been enacted uponwhen compared to its parent function,?
vertical stretch by a factor of 4
horizontal compression by a factor of 2
horizontal translation 6 units right
vertical stretch by a factor of 4
horizontal stretch by a factor of 2
horizontal translation 6 units right
vertical stretch by a factor of 4
horizontal compression by a factor of 2
horizontal translation 3 units right
vertical stretch by a factor of 4
horizontal stretch by a factor of 2
horizontal translation 3 units right
vertical stretch by a factor of 4
horizontal compression by a factor of 2
horizontal translation 3 units right
First, we need to get this function into a more standard form.
Now we can see that while the functionisbeing horizontally compressed by a factor of 2, it's being translated 3 units to the right, not 6. (It's also being vertically stretched by a factor of 4, of course.)
Example Question #53 :Polynomial Functions
Defineand.
Find.
By definition,, so
Example Question #3 :Transformations Of Polynomial Functions
Defineand.
Find.
By definition,, so
Example Question #1 :Transformations Of Polynomial Functions
Write the transformation of the given function moved five units to theleft:
To transform the function horizontally, we must make an addition or subtraction to the input, x. Because we are asked to move the function to the left, we must add the number of units we are moving. This is the opposite of what one would expect, but if we are inputting values that are to the left of the original, they arelessthan what would have originally been. So, to counterbalance this, weaddthe units of the transformation.
For our function being transformed five units to the left, we get
Example Question #1 :Transformations Of Polynomial Functions
Write the transformation of the given function flipped, and moved one unit to the left:
To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, weaddunits to x, which is opposite what one thinks should happen, but keep in mind that to move left is to be more negative. To flip a function, the entire function changes in sign.
After making both of these changes, we get
Example Question #6 :Transformations Of Polynomial Functions
Transform the function by moving it two units up, and five units to the left:
To transform a function we use the following formula,
where h represents the horizontal shift and v represents the vertical shift.
In this particular case we want to shift to the left five units,
and vertically up two units,
.
Therefore, the transformed function becomes,
.
Example Question #2 :Transformations Of Polynomial Functions
Shiftup one unit. What is the new equation?
Expand the binomial.
Multiply negative by this quantity.
The polynomial in standard form is:
Shifting this graph up one will change the y-intercept by adding one unit.
The answer is:
Example Question #8 :Transformations Of Polynomial Functions
Shift the graphup two units. What's the new equation?
Shifting this parabola up two units requires expanding the binomial.
Use the FOIL method to simplify this equation.
Shifting this graph up two units will add two to the y-intercept.
The answer is:
Example Question #9 :Transformations Of Polynomial Functions
Shiftto up two units. What is the new equation?
We will need to determine the equation of the parabola in standard form, which is:
使用箔方法来扩大二项式。
Shifting this up two units will add two to the value of.
The answer is:
Example Question #10 :Transformations Of Polynomial Functions
Ifand, what is?
In this problem, thein theequation becomes-->.
This simplifies to, or
.
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