Question

Please help (question given in file)

Answer 1

`y = x +3` if
`-3 \leq x <-1`

`y = 5` if
`-1 \leq x \leq 1`

Explanation:

The piecewise function is made up of two linear functions.

1) A line of positive slope that passes through the points (-3, 0) and (-1, 2)

2) A straight line with slope m = 0.

For the first line we have 2 points (-3, 0) and (-1, 2)

Then we can find the slope m.

`m = (y_2 -y_1)/(x_2 - x_1)\\\\m = (2-0)/(-1 -(-3))\\\\m = 1`

Then the equation is:

`y = x + b`

Now we find b substituting a point in the equation

`0 = -3 + b\\b = 3`

Then the equation is:

`y = x +3`

Notice that this equation goes from x = -3 to x = -1. Not including -1.

Then the second line cuts the y-axis at y = 5 and its slope is m = 0.

Then your equation is:

`y = 5`

Finally, the piecewise function is:

`y = x +3` if
`-3 \leq x <-1`

`y = 5` if
`-1 \leq x \leq 1`