Question

Please help (question given in file)

Answer 1

Answer:

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

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

Step-by-step 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.

$m = \frac{y_2 -y_1}{x_2 - x_1}\\\\m = \frac{2-0}{-1 -(-3)}\\\\m = 1$

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 $-1 \leq x \leq 1$