Question

Help me find the answer to this piecewise problem!! 20 Points !!!!

Answer 1

So we have x+3 if -3<=x<=-1

and 5 if -1<=x<=1

Explanation:

The one piece from -1 to 1 is horizontal so the line is in the form of y=a number. It goes through 5 on the y-axis so the equation there is y=5.

From -3 to -1, that is a line with positive slope (since that part is increasing).

Slope=rise/run

We see from the filled in dot to the unfilled in dot that the rise is 2 and the run is 2 so the slope is 2/2=1.

So if we did extend this line where we go at on the y-axis? It would go through 3 because starting from the unfilled dot and rising 1 and running 1 will get us to the 3 on the y-axis.

The equation of a line in slope-intercept form is y=mx+b.

We have m=1 and b=3 so the equation is y=1x+3 or just y=x+3.

So we have x+3 if -3<=x<=-1

and 5 if -1<=x<=1

Answer 2

`\large\boxed{f(x)=\left\{\begin{array}{ccc}x+3&,\ \text{if}\ -3\leq x<-1\\5&,\ \text{if}\ -1\leq x\leq1\end{array}\right}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

Read coordinates of the two points on the first piece:

(-3, 0) and (-2, 1).

Calculate the slope:

`m=(1-0)/(-2-(-3))=(1)/(1)=1`

Put it and coordinates of the point (-3, 0) to the equation of a line:

`0=1(-3)+b`

`0=-3+b` add 3 to both sides

`3=b\to b=3`

`\boxed{y=x+3}`

Read coordinates of the two points on the second piece:

(-1, 5) and (1, 5) - second coordinates are the same.

It's a horizontal segment. Therefore the equation is
`y=5`