WORKSHEET ON FUNCTION TRANSFORMATIONS

Problem 1 : 

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

Problem 2 :

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

Problem 3 : 

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

Problem 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 ?

Problem 5 : 

Submit an equation that will move the graph of the function y = x2  to the point (-3, 1).

Problem 6 : 

The equation y = (x + 3)2 – 2 moves the vertex of the parent function y = x2 to :

Problem 7 : 

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

Problem 8 : 

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

True or False ?

Solutions

Problem 1 : 

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

Solution : 

From the parent function y = x2, 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)- 3

Problem 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

Solution : 

In the parent function y = x2, 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+ 9

So, option "C" is correct.

Problem 3 : 

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

Solution : 

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

Problem 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 ?

Solution : 

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.

So, it is true.

Problem 5 : 

Submit an equation that will move the graph of the function y = x2  to the point (-3, 1). 

Solution : 

The vertex of the parent equation y = x2 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 = x2 is moved 3 units left and 1 unit up.

In the parent function y = x2, 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

Problem 6 : 

The equation y = (x + 3)2 – 2 moves the vertex of the parent function y = x2 to :

(a) (3, 2)

(b) (-3, -2)

(c) (-2, 3)

(d) (2, -3)

Solution : 

When we compare the parent function y = x2 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).

The equation y = (x + 3)2 - 2 moves the vertex of the parent function y  =  x2 to (-3, -2)

So, option "B" is correct.

Problem 7 : 

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

Solution : 

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

Problem 8 : 

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

True or False ?

Solution : 

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.

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