Answer:
The function representing the graph is described by two equations, depending on the "x" value
f(x) = (1/3)x + 3 , if x is greater than -3.
f(x) = -x - 5 , if x is less than -3.
Step-by-step explanation:
First, you have to realize that the graph is described by two functions depending on the "x" value and that it is not defined in x= -3.
Then, for "x" values greater than -3, we look at the right line and we took 2 couple of points (-3,2) and (0,3). Using the formula for the slope and the interception with y axis.....
Slope = y2- y1 / x2- x1 = 3 - 2/ 0 - (-3) ⇒ slope = 1/3.
Interception with "y" axis y= 3
⇒ f(x) = (1/3) x + 3.
For "x" values minor than -3, we have to look the left line. Here we used the slope formula and points (-3, -2) and (-5, 0)
Slope = 0 - (-2)/ -5 - (-3) =-1. So, f(x) = -x + b.
Finally we use one of the points to replace in the formula of f(x) to find "b".
-2 = - (-3) + b ⇒ b = -5. ⇒ f(x) = - x -5
Summarizing, f(x) = (1/3)x + 3 , if x is greater than -3.
f(x) = -x - 5 , if x is less than -3.
