Math Problem Statement

Evaluate f(3) and solve f(x) = 3 using the given plot of f(x).

Solution

The image shows a problem involving the evaluation of a function f(x)f(x) based on a plot, and you are tasked with evaluating f(3)f(3) and solving f(x)=3f(x) = 3.

Steps to Solve:

  1. Evaluate f(3)f(3):

    • From the graph, locate x=3x = 3 on the x-axis.
    • Observe the corresponding value of f(x)f(x) (i.e., the y-value) at that point. From the plot, it appears that f(3)=6f(3) = 6.
  2. Solve f(x)=3f(x) = 3:

    • To find the x-value when f(x)=3f(x) = 3, look for the points on the graph where the y-value is 3.
    • From the graph, the curve intersects f(x)=3f(x) = 3 at x=1x = 1.

Thus:

  • f(3)=6f(3) = 6
  • x=1x = 1 when f(x)=3f(x) = 3.

Let me know if you need more details, and here are a few related questions:

  1. What is the domain and range of this function based on the graph?
  2. Can you explain how to determine if this function is increasing or decreasing?
  3. How would you use function notation to describe shifts in the graph?
  4. What are the intercepts of this function?
  5. How do you check if this function is one-to-one?

Tip: When working with graphs, always check the corresponding x and y values carefully to avoid misreading points.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Interpretation
Function Evaluation

Formulas

None (based on graph interpretation)

Theorems

None (based on graph interpretation)

Suitable Grade Level

Grade 9-10 (Algebra)