Transformations of Polynomial Functions - Algebra 2
Card 0 of 40
What transformations have been enacted upon 
when compared to its parent function, 
?
What transformations have been enacted upon
Tap to see back →
First, we need to get this function into a more standard form.
Now we can see that while the function is being 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.)
First, we need to get this function into a more standard form.
Now we can see that while the function is being 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.)
If 
and 
, what is 
?
If
Tap to see back →
In this problem, the 
in the 
equation becomes 
--> 
.
This simplifies to 
, or
.
In this problem, the
This simplifies to
Define 
and 
.
Find 
.
Define
Find
Tap to see back →
By definition, 
, so
By definition,
Define 
and 
.
Find 
.
Define
Find
Tap to see back →
By definition, 
, so
By definition,
Write the transformation of the given function moved five units to the left:
Write the transformation of the given function moved five units to the left:
Tap to see back →
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 are less than what would have originally been. So, to counterbalance this, we add the units of the transformation.
For our function being transformed five units to the left, we get
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 are less than what would have originally been. So, to counterbalance this, we add the units of the transformation.
For our function being transformed five units to the left, we get
Transform the function by moving it two units up, and five units to the left:
Transform the function by moving it two units up, and five units to the left:
Tap to see back →
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,
.
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,
Write the transformation of the given function flipped, and moved one unit to the left:
Write the transformation of the given function flipped, and moved one unit to the left:
Tap to see back →
To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, we add units 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
To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, we add units 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
Shift 
up one unit. What is the new equation?
Shift
Tap to see back →
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: 
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:
Shift the graph 
up two units. What's the new equation?
Shift the graph
Tap to see back →
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: 
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:
Shift 
to up two units. What is the new equation?
Shift
Tap to see back →
We will need to determine the equation of the parabola in standard form, which is:
Use the FOIL method to expand the binomials.
Shifting this up two units will add two to the value of 
.
The answer is: 
We will need to determine the equation of the parabola in standard form, which is:
Use the FOIL method to expand the binomials.
Shifting this up two units will add two to the value of
The answer is:
What transformations have been enacted upon when compared to its parent function, ?
What transformations have been enacted upon
Tap to see back →
First, we need to get this function into a more standard form.
Now we can see that while the function is being 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.)
First, we need to get this function into a more standard form.
Now we can see that while the function is being 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.)
If and , what is ?
If
Tap to see back →
In this problem, the in the equation becomes --> .
This simplifies to , or
.
In this problem, the
This simplifies to
Define and .
Find .
Define
Find
Tap to see back →
By definition, , so
By definition,
Define and .
Find .
Define
Find
Tap to see back →
By definition, , so
By definition,
Write the transformation of the given function moved five units to the left:
Write the transformation of the given function moved five units to the left:
Tap to see back →
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 are less than what would have originally been. So, to counterbalance this, we add the units of the transformation.
For our function being transformed five units to the left, we get
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 are less than what would have originally been. So, to counterbalance this, we add the units of the transformation.
For our function being transformed five units to the left, we get
Transform the function by moving it two units up, and five units to the left:
Transform the function by moving it two units up, and five units to the left:
Tap to see back →
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,
.
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,
Write the transformation of the given function flipped, and moved one unit to the left:
Write the transformation of the given function flipped, and moved one unit to the left:
Tap to see back →
To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, we add units 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
To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, we add units 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
Shift up one unit. What is the new equation?
Shift
Tap to see back →
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:
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:
Shift the graph up two units. What's the new equation?
Shift the graph
Tap to see back →
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:
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:
Shift to up two units. What is the new equation?
Shift
Tap to see back →
We will need to determine the equation of the parabola in standard form, which is:
Use the FOIL method to expand the binomials.
Shifting this up two units will add two to the value of .
The answer is:
We will need to determine the equation of the parabola in standard form, which is:
Use the FOIL method to expand the binomials.
Shifting this up two units will add two to the value of
The answer is: