Answer:
Explanation:
Looking at the graph we can see that it is a linear graph of the form
y = mx + b where m is the slope and b is the y intercept.
In one region the slope is positive and the other region it is negative
Interval 1 is -6 ≤ x < -3
How do I know that one uses a ≤ and the other uses a <?
A filled circle means that the point is included in the domain(range of x values) and therefore (≤, ≥) and an unfilled circle means it is not(<, >)
Find the slope of line in this interval
Take two points, say (-5, 0) and (-3, 4)
Slope = rise/run = (4 - 0)/(-3 - (-5) = 4/2 = 2
So slope of line is 2 and its equation in slope-intercept form is
y = 2x + b
Choose any point, plug in values, solve for b
Point (5, 0) is chosen
0 = 2(-5) + b
0 = -1 + b
or
b = 10
So equation of line in the interval (-6 ≤ x < -3) is
y = f(x) = 2x + 10
Interval 2: -3 < x < 2
We see this line intersects the y axis at y = 1
So b = 1
Equation is y = mx + 1
Choose point x = 0, y = 1 to find slope m
At x = 0, y = m(1) + 1 = m + 1
So m + 1 = 0
m = -1
So equation of this line is
y = f(x) = -1x + 1 in the interval -3 < x < 2
Putting all these together we get the piecewise function as: