Question

The graph represents the piecewise function. Type the answer in the boxes below.

Answer 1

`f(x)=\left\{\begin{matrix}2x &\text{ if }-3\leq x\leq -1\\3 &\text{ if }(1)/(2)<x<(3)/(2)\end{matrix}\right.`

Explanation:

We are given a graph of piecewise function. We need to find the function of graph.

Here we have two piece of graph. We will find the equation of graph one by one.

First we take left side of y and bottom of x.

We can a line passes through two point (-3,-6) and (0,0)

Using two point for find the equation of line.

`y-0=(0+6)/(0+3)(x-0)`

`y=2x` If
`-3\leq x\leq 0`

Now we find equation of second piece which is right of y and above x-axis.

It is horizontal line. Equation of horizontal line is y=k. If we extent the line k would be 3.

Equation of second piece:
`y=3` if
`(1)/(2)<x<(3)/(2)`

Now we write piece wise function combined form.

`f(x)=\left\{\begin{matrix}2x &\text{ if }-3\leq x\leq -1\\3 &\text{ if }(1)/(2)<x<(3)/(2)\end{matrix}\right.`