FUNCTION TRANSFORMATIONS WORKSHEET

Problem 1 : 

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

Problem 2 :

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

Problem 3 : 

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

Problem 4 : 

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

Problem 5 : 

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

Problem 6 : 

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

Problem 7 : 

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

Problem 8 : 

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

Problem 1 : 

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

Solution : 

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

Problem 2 :

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

True or False ?

Solution : 

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.

Problem 3 : 

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

Solution : 

When we move the graph of the equation y = x² down 7 units, we will get the graph with the equation.

y = x² - 7

Problem 4 : 

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

True or False ?

Solution : 

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.

Problem 5 : 

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

Solution : 

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

Problem 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 

Solution : 

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

So, option "c" is correct.

Problem 7 : 

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

Solution : 

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

Problem 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

Solution : 

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

So, option "d" is correct.

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