Math Problem Statement

using the first image as an example solve the equation on the second image

Using the first image as an example solve the equation on the second image

Solution

To solve the equation in the second image, which asks to find the value of f(3)f(-3) based on the graph of y=f(x)y = f(x), we will follow the same approach used in the first image example.

Steps:

  1. Locate x=3x = -3 on the horizontal axis.

    • On the graph, find the point where x=3x = -3.
  2. Determine the corresponding yy-value.

    • Find the point on the graph at x=3x = -3 and trace vertically to where it intersects the curve y=f(x)y = f(x).
  3. Read the yy-coordinate.

    • At x=3x = -3, the curve reaches a yy-value of 44.

Solution:

Thus, f(3)=4f(-3) = 4.

Do you want further details or have any questions about the solution?


Here are 5 related questions:

  1. How do you find f(x)f(x) for any given value of xx from a graph?
  2. What is the significance of the maximum point on the graph of y=f(x)y = f(x)?
  3. How do you determine the symmetry of a graph like this?
  4. Can you explain what the xx-intercepts represent for the function f(x)f(x)?
  5. What would f(0)f(0) be based on the second graph?

Tip: When analyzing a graph, always double-check the axis scales to ensure correct xx- and yy-coordinate interpretation.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Analysis
Quadratic Functions

Formulas

None - Graphical Interpretation

Theorems

None explicitly required, but understanding of function behavior and graphing principles

Suitable Grade Level

Grades 8-10