Question

6. Refer to the graph in question 5A) graph -f(x)B) graph f(x) -2

Answer 1

Given the graph of f(x):

Where the points A, B, and C have the coordinates:

`\begin{gathered} A=(0,-2) \\ B=(3,2) \\ C=(5,2) \end{gathered}`

Now, the transformation -f(x) is just a reflection about the x-axis. This is equivalent to a change of sign on the y-coordinate. The new points A', B', and C' are:

`\begin{gathered} A^(\prime)=(0,2) \\ B^(\prime)=(3,-2) \\ C^(\prime)=(5,-2) \end{gathered}`

And the graph looks like this:

Now, for the f(x) - 2 transformation, we see that this is just a shift of 2 units down. Then:

Where:

`\begin{gathered} A^(\prime)^(\prime)=(0,-4) \\ B^(\prime)^(\prime)=(3,0) \\ C^(\prime)^(\prime)=(5,0) \end{gathered}`