Question

Write a definition for the function that best describes this graph.

Answer 1

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:

`\begin{gathered} m=(y2-y1)/(x2-x2) \\ \\ m=(0-2)/(0-(-1))=(-2)/(1)=-2 \end{gathered}`

Therefore, the equation is:

y = -2x

• Equation of line segments with endpoints (3, 1) and (0, 0);

`m=(0-1)/(0-3)=(-1)/(-3)=(1)/(3)`

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