Question

5.Consider the piecewise function A graph the functionB list the interceptsC find f(1)D f(2)

Answer 1

Graphing

We can use a graphing calculator to give us a visual representation of what the piecewise function looks like:

Listing Intercepts

We can find the x and y-intercepts by looking at the graph.

The x-intercepts are where the piecewise function crosses the x-axis.

• x = 0.5

The y-intercepts are where the piecewise function crosses the y-axis.

• y = -1

Finding f(1)

We can directly use the mathematical function to find f(1).

Since 1 is less than 2, we will have to use the top equation of the piecewise function:

$\begin{gathered} f(1)=2(1)-1,1<2 \\ f(1)=2-1,1<2 \\ f(1)=1,1<2 \end{gathered}$

Therefore, f(1) = 1.

Finding f(2)

We can use the same method as the section above.

Since 2 is equal to 2, we will have to use the bottom equation of the piecewise function:

$\begin{gathered} f(2)=2+3,2\ge2 \\ f(2)=5,2\ge2 \end{gathered}$

Therefore, f(2) = 5.