Given the points on the graph:
(x, y) ==> (-1, 2), (0, 0), and (3, 1)
The graph represents a piece-wise function.
Let's write a definition for the function that best describes the graph.
Using the points, we have:
• (-1, 2) ==> f(x) = 2, when x = -1
,
• (3, 1) ==> f(x) = 1, when x = 3
Let's find the equation of each line.
• Equation of line segment with endpoints (-1, 2) and (0, 0)
Apply the slope intercept form:
y = mx + b
Use the slope formula to find the slope:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x2} \\ \\ m=\frac{0-2}{0-(-1)}=\frac{-2}{1}=-2 \end{gathered}[/tex]
Therefore, the equation is:
y = -2x
• Equation of line segments with endpoints (3, 1) and (0, 0);
[tex]m=\frac{0-1}{0-3}=\frac{-1}{-3}=\frac{1}{3}[/tex]
Therefore, the equation is:
y = 1/3x
Hence, the definition for the functions that best describe the left piece of the graph is:
f(x) = -2x, if -1 ≤ x ≤ 0
The definition for the right piece of the function is:
f(x) = 1/3x, if 0 ≤ x ≤ 3
ANSWER:
f(x) = -2x, if -1 ≤ x ≤ 0
