Math Problem Statement

Evaluate the function graphically. Find f(8) using the provided graph.

Solution

To evaluate f(8)f(8) graphically using the provided image:

  1. Look for the xx-coordinate of 8 on the graph.
  2. Locate the corresponding point on the function. From the graph:
    • The open circle at (8,3)(8, -3) means that f(8)f(8) is not defined at y=3y = -3.
    • The filled circle at (8,6)(8, -6) indicates the actual value of the function at x=8x = 8.

Thus, f(8)=6f(8) = -6.


Would you like further clarification or details on this?
Here are five related questions for practice:

  1. How do open and closed circles affect the value of a function?
  2. How can you determine if a function is continuous at a given point?
  3. What does f(a)f(a) represent graphically?
  4. How can you evaluate f(x)f(x) for other points using this graph?
  5. What is the difference between evaluating f(8)f(8) and finding the limit as x8x \to 8?

Tip: Always check whether the point is included (closed circle) or excluded (open circle) when interpreting a graph!

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Math Problem Analysis

Mathematical Concepts

Function evaluation
Graph interpretation
Open and closed circles in graphs

Formulas

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Theorems

Definition of a function
Graphical representation of a function

Suitable Grade Level

Grades 8-10