"Function transformations worksheet 1" is the one in which students can review what they have studied about function 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 1, we have provided 8 questions along with their answers.

**1. Submit an equation that will move the graph of the function y=x****² left 7 units and down 3 units.**

From the parent function y = x^{2}, if it is moved 7 units to the left, we will have the function y = (x+7)^{2}.

Further, if it is moved 3 units down, the function will be

y = (x+7)^{2}-3.

Further, if it is moved 3 units down, the function will be

y = (x+7)

**2. Which equation will shift the graph of y = x² up 9 units ? **

**(a) y = (x+9)²**

**(b) y = x² - 9**

**(c) y = x² + 9**

**(d) y = (x-9)² **

In the parent function y = x^{2}, if it is moved units up, we have to add 9 on the right side of the function.

After having applied the given translation, the function will be y = x^{2}+9.

Hence option "C" is correct.

After having applied the given translation, the function will be y = x

Hence option "C" is correct.

**3. Submit an equation that will move the graph of the function y=log(x) right 4 units and up 6 units.**

When we move the graph of the equation y = log(x) to the right 4 units, we have to subtract 4 from "x".

Then the equation will be y = log (x-4).

Further, if it is moved 6 units up, we have to add 6 on the right side of the equation.

Then the equation will be y = log (x-4) + 6.

Then the equation will be y = log (x-4).

Further, if it is moved 6 units up, we have to add 6 on the right side of the equation.

Then the equation will be y = log (x-4) + 6.

**4. ****The equation y = log(x-3) + 9 moves the parent function y = log(x) right 3 units and up 9 units.**

**True or False**

In the parent function y = log(x), if it is moved 3 units right, we have to subtract 3 from "x".

Then the function will be y = log(x-3)

Further, if it is moved 9 units up, we have to add 9 on the right of the function.

Then the function will be y = log(x-3) + 9.

The answer given in the question is also the same, Hence, it is true.

Then the function will be y = log(x-3)

Further, if it is moved 9 units up, we have to add 9 on the right of the function.

Then the function will be y = log(x-3) + 9.

The answer given in the question is also the same, Hence, it is true.

**5. ****Submit an equation that will move the vertex of the function y=x****² to the point (-3,1).**

The vertex of the parent equation y = x^{2} is (0,0).This vertex is moved to (-3,1)

When we compare the "x" co-ordinates of (0,0) and (-3,1), clearly, the vertex is moved 3 units to the left.

When we compare the "y" co-ordinates of (0,0) and (-3,1), clearly the vertex is moved 1 unit up.

From the above argument, it is clear that the parent equation y = x^{2} is moved 3 units left and 1 unit up.

In the parent function y = x^{2}, if it is moved 3 units to the left, we have to add 3 to "x".

Then the function will be y = (x+3)^{2}

Further, if it is moved 1 unit up, we have to add 1 on the right side of the equation.

Then the function will be y = (x+3)^{2} + 1.

When we compare the "x" co-ordinates of (0,0) and (-3,1), clearly, the vertex is moved 3 units to the left.

When we compare the "y" co-ordinates of (0,0) and (-3,1), clearly the vertex is moved 1 unit up.

From the above argument, it is clear that the parent equation y = x

In the parent function y = x

Then the function will be y = (x+3)

Further, if it is moved 1 unit up, we have to add 1 on the right side of the equation.

Then the function will be y = (x+3)

**6. The equation y = (x+3)****² – 2 moves the vertex of the parent function y = x****² to:**

**(a) (3,2)**

**(b) (-3,-2)**

**(c) (-2,3)**

**(d) (2,-3)**

When we compare the parent function y = x^{2} and the equation

y = (x+3)^{2} - 2, we see that the parent function is moved 3 units left and 2 units down.

The vertex of the parent function is (0,0). If it is moved 3 units left and 2 units up, the new vertex will be (-3,-2).

Hence the equation y = (x+3)^{2} - 2 moves the vertex of the parent function y = x^{2} to (-3,-2)

Hence option "B" is correct.

y = (x+3)

The vertex of the parent function is (0,0). If it is moved 3 units left and 2 units up, the new vertex will be (-3,-2).

Hence the equation y = (x+3)

Hence option "B" is correct.

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

In the given equation y = |x|, if it is moved 2 units left, we have to add 2 to "x".

Then, the equation will be y = |x+3|

Further, if it is moved 5 units right, we have to add 5 on the right of the equation.

Then the equation will be y = |x+3| + 5.

Then, the equation will be y = |x+3|

Further, if it is moved 5 units right, we have to add 5 on the right of the equation.

Then the equation will be y = |x+3| + 5.

**8. The equation y = |x - 4| - 5 moves the parent function y = |x| right 5 units and down 4 units.**

**True or False**

In the parent function y = |x|, if it is moved 5 units right, we have to subtract 5 from "x".

Then the equation will be y = |x-5|.

Further, if it is moved 4 units down, we have to subtract 4 on the left side of the equation.

Then, the equation will be y = |x-5| - 4

But, the answer given in the question is y = |x-4| -5. This is different from the correct answer.

So, it is false.

Then the equation will be y = |x-5|.

Further, if it is moved 4 units down, we have to subtract 4 on the left side of the equation.

Then, the equation will be y = |x-5| - 4

But, the answer given in the question is y = |x-4| -5. This is different from the correct answer.

So, it is false.

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