"Function transformations worksheet" is the one in which students can review what they have studied about functions transformations. This review is made by the students to make sure that they have understood different types of translations of functions.

This review has to be made by each and every student after having studied the different concepts in function translations.

The different types of translations are

__1. Horizontal translation (Right or Left)__

Let **y = f(x)** be a function and "**k**" be a constant.

In the above function, if **"x"** is replaced by **"x-k"** , we get the new function **y = f(x-k)**.

The graph of y= f(x-k) can be obtained by the translating the graph of y = f(x) to the right by **"k"** units if **"k" is a positive number**.

In case **"k" is a negative number**, the graph of y = f(x) will be translated to the left by **|k|** units.

Moreover, if the the point **(x,y)** is on the graph of y = f(x), then the point **(x+k , y)** is on the graph y = f(x-k).

For example, if **k =3**, the graph of y = f(x) will be translated to the right by **"3"** units.

If **k = -3**, the graph of y = f(x) will be translated to the left by **"3"** units.

**2. Vertical translation (Up or Down)**

Let **y = f(x)** be a function and "**k**" be a positive number.

In the above function, if **"y"** is replaced by **"y-k"** , we get the new function **y - k = f(x) **or** y = f(x) + k. **

The graph of y= f(x) + k can be obtained by translating the graph of y = f(x) towards upward by **"k"** units.

In case, **"y"** is replaced by **"y + k"** , we get the new function

**y + k = f(x) **or** y = f(x) - k. **

The graph of y= f(x) - k can be obtained by translating the graph of y = f(x) towards downward by **"k"** units.

Moreover, if the the point **(x,y)** is on the graph of y = f(x), then the point **(x , y+k)** is on the graph y = f(x)+k

Even though students can get functions translations review worksheets on internet, they do not know that the answers they have received for the questions are correct or wrong.

Here step by step explanations are given for each and every question to make the students to understand the concepts thoroughly.

Before going to the questions, please learn about horizontal and vertical translations clearly.

**Click here to know more about horizontal translation **

**Click here to know more about vertical translation**

In this function transformations worksheet, we have provided 8 questions along with their answers.

**1. Submit an equation that will move the graph of the function y=x² right 4 units.**

As per the rule, if the graph is moved 4 units to the right, we have to subtract 4 from "x" in the parent function.

After having applied the given translation, the function is

y = (x-4)^{2}

After having applied the given translation, the function is

y = (x-4)

**2.The equation y = (x+3)² – 2 moves the parent function y = x****²** right 3 units and down 2 units.

**True or False**

From the parent function y = x^{2}, if it is moved 3 units right, we will have the function y = (x-3)^{2}.

Further, if it is moved 2 units down, the function will be

y = (x-3)^{2}-2.

But the given answer is y = (x+3)^{2}-2.

So, it is false.

Further, if it is moved 2 units down, the function will be

y = (x-3)

But the given answer is y = (x+3)

So, it is false.

**3. Submit an equation that will move the graph of the function y = x² down 7 units.**

When we move the graph of the equation y = x^{2} down 7 units, we will get the graph with the equation y = x^{2}-7

**4. The equation y = (x-8)² + 5 moves the parent function y = x****² right 8 units and down 5 units.**

**True or False**

When we move the parent function y = x^{2} to the right 8 units, we will have the equation y = (x-8)^{2}.

Further, if its moved 5 units down, the equation will be y = (x-8)^{2}-5.

But, the given answer is y = (x-8)^{2}+5.

So, it is false.

Further, if its moved 5 units down, the equation will be y = (x-8)

But, the given answer is y = (x-8)

So, it is false.

**5. Submit an equation that will move the graph of the function y=x² left 2 units and up 6 units.**

In the given function y = x^{2}, if it is moved 2 units left, we will have the function, y = (x+2)^{2}.

Further, if it is moved 6 units up, the function will be y = (x+2)^{2} + 6

Further, if it is moved 6 units up, the function will be y = (x+2)

**6. Which equation will shift the graph of y = x² left 5 units and up 6 units?**

**(a) y = (x+6)² - 5**

**(b) y = (x+5)² - 6**

**(c) y = (x+5)² + 6**

**(d) y = (x-5)² + 6 **

In the given function y = x^{2}, if it is moved 5 units left, we will have the function, y = (x+5)^{2}.

Further, if it is moved 6 units up, the function will be y = (x+5)^{2} + 6

Hence, option "c" is correct.

Further, if it is moved 6 units up, the function will be y = (x+5)

Hence, option "c" is correct.

**7. Submit an equation that will move the graph of the function y=x² right 3 units up 2 units.**

In the given function y = x^{2}, if it is moved 3 units right, we will have the function, y = (x-3)^{2}.

Further, if it is moved 2 units up, the function will be y = (x-3)^{2} + 2

Further, if it is moved 2 units up, the function will be y = (x-3)

**8. Which equation will shift the graph of y = x² right 8 units and down 4 units?**

**(a) y = (x+8)² - 4**

**(b) y = (x+4)² - 8**

**(c) y = (x-4)² + 8**

**(d) y = (x-8)² - 4 **

In the given function y = x^{2}, if it is moved 8 units right, we will have the function, y = (x-8)^{2}.

Further, if it is moved 4 units down, the function will be y = (x-8)^{2} - 4

Hence, option "d" is correct.

Further, if it is moved 4 units down, the function will be y = (x-8)

Hence, option "d" is correct.

**Click here to get more questions on function tranformations**

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