Math Problem Statement

Evaluate f(3) using the graph of the function f(x).

Solution

I see that you are working on a question related to evaluating the function f(x)f(x) using a graph in your College Algebra course. The question asks you to evaluate f(3)f(3), meaning you need to find the value of the function at x=3x = 3 by looking at the graph.

Here’s how you can solve it:

  1. Look for the point on the graph where x=3x = 3 on the x-axis.
  2. Find the corresponding value of f(x)f(x) (the y-value) at that x=3x = 3.

Let me check the graph for you:

  • From what I can see in the graph, when x=3x = 3, the function appears to give a value of f(3)=2f(3) = -2.

Thus, f(3)=2f(3) = -2.

Would you like a more detailed breakdown of this process? Here are a few related questions to think about:

  1. How can you determine the output of a function from its graph for different values of xx?
  2. How do you recognize whether a function is increasing or decreasing from its graph?
  3. What are some common characteristics of the graph of a quadratic function versus a linear function?
  4. How can you find intercepts (x- and y-intercepts) from a graph?
  5. What does the slope of a line segment tell you about the behavior of the function?

Tip: When evaluating a function from a graph, always make sure to trace carefully along the x-axis to find the correct output on the y-axis!

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Math Problem Analysis

Mathematical Concepts

Functions
Graphing
Function Evaluation

Formulas

f(x) represents the output of the function for a given input x.

Theorems

A function maps each input to exactly one output.

Suitable Grade Level

Grades 9-12