Question

6. Sketch the graph of each of the following. Describe the transformation in each graph a. g(x) = f(x) - 1 b. h(x) = -f(x)

Answer 1

Part A

g(x)=f(x)-1

In order to obtain g(x), f(x) was translated 1 unit downwards.

A sketch of the graph is given below.

Part B

h(x)=-f(x)

In order to obtain h(x), f(x) was reflected across the x-axis.

A sketch of h(x) is given below:

Part C

p(x)=f(x+2)

In order to obtain p(x), f(x) was translated left by 2 units.

A sketch of p(x) is given below:

Part D

q(x)=-f(x+2)-1

n order to obtain q(x), f(x) was reflected across the x-axis, translated by 2 units to the left and 1 unit down.

The new points are:

`\begin{gathered} (4,2)\to(4,-2)\to(4-2,-2-1)=(2,-3) \\ (-3,1)\to(-3,-1)\to(-3-2,-1-1)=(-5,-2) \end{gathered}`

A sketch of q(x) is given below: