# FUNCTION TRANSFORMATIONS WORKSHEET

## About the topic "Function transformations worksheet"

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

## Horizontal and vertical translations - review questions

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

jQuery UI Accordion - Default functionality
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

2.The equation y = (x+3)² – 2 moves the parent function           y = x²  right 3 units and down 2 units.

True or False

jQuery UI Accordion - Default functionality
From the parent function y = x2, 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.

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

jQuery UI Accordion - Default functionality
When we move the graph of the equation y = x2 down 7 units, we will get the graph with the equation y = x2-7

4. The equation y = (x-8)² + 5 moves the parent function       y = x²  right 8 units and down 5 units.

True or False

jQuery UI Accordion - Default functionality
When we move the parent function y = x2 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.

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

jQuery UI Accordion - Default functionality
In the given function y = x2, 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

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

jQuery UI Accordion - Default functionality
In the given function y = x2, 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.

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

jQuery UI Accordion - Default functionality
In the given function y = x2, 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

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

jQuery UI Accordion - Default functionality
In the given function y = x2, 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.