Question

Create a table of values and sketch a graph of the piecewise function. Be sure to use the correct notation to indicate any start/end points on your graph.Label your x and y axis with your increments.Identify the domain and range using interval notation. f(x) = \left\lbrace \begin{array}{cc} y=3 & x<0 \\ x+1 & x\ge 0 \end{array}\right.

Answer 1

We need to graph a piecewise function, there are two expressions and we need to respect the correct intervals.

For negative values of "x", the expression is "y=3", therefore this graph is a constant line at -3.

We need to insert a opened dot at "x=0", because the signal used is "<".

For positive values and for "x=0", we need to use the expression "x+1". This is a linear equation, to graph it, we need to find two points. We will look for the points at which "x = 0" and x"=1". We have:

`\begin{gathered} f(0)=0+1=1 \\ f(1)=1+1=2 \end{gathered}`

We need to mark these two points at the graph and draw the line between them: