Question

The graph of the function y=h(x) is given below A) State in correct order the transformations that must be performed to graph the function: y=2h(x+4)+3 B) Graph y=2h(x+4)+3 and label the coordinates of three points on the graph

Answer 1

Transformations of Functions

We are given the graph of a function y=h(x).

A)

We must apply transformations to get the funcion:

y=2h(x + 4) + 3

The first transformation must be a translation by 4 units to the left. That will give us h(x + 4).

Secondly, we must stretch the function obtained above by a factor of 2 to get:

2h(x + 4).

Finally, we must translate the function above by 3 units up and get the required result:

y=2h(x + 4) + 3

B)

Let's call the points of the original function:

P(-2,-1) Q(0,1) R(2,-3)

Now we map those points to the transformed points by using the rules:

Translate 4 units left

Stretch by a factor of 2

Translate 3 units up

The point P has x=-2 and will map to:

y = 2(-2+4)+3 = 2(2) + 3 = 7

P'(-2,7)

The point Q has x=0 and will map to:

y = 2(0+4)+3 = 2(4) + 3 = 11

Q'(0,11)

The point R has x=2 and will map to:

y = 2(2+4)+3 = 2(6) + 3 = 15

P'(2,15)

We use the mapped points to produce the new graph as follows: