Math Problem Statement

Find the value of f(-3).

Solution

The image shows a question asking to find the value of f(3)f(-3) from a graph of the function y=f(x)y = f(x).

To find f(3)f(-3):

  1. Look for the value of x=3x = -3 on the x-axis.
  2. Trace upward or downward to the curve of the graph.
  3. Read the corresponding value of yy where the graph intersects.

From the graph, when x=3x = -3, the value of yy appears to be 4. Therefore:

f(3)=4f(-3) = 4

Would you like more details, or do you have any further questions?

Here are 5 related questions to consider:

  1. What is the general shape of the graph, and how does it relate to quadratic functions?
  2. How do you determine the domain and range of this function based on the graph?
  3. What happens to the value of f(x)f(x) as xx approaches positive or negative infinity?
  4. What is the vertex of this parabola, and what does it tell us about the function?
  5. How can we algebraically determine f(x)f(x) if the equation of the parabola is known?

Tip: When analyzing functions from a graph, always check key points such as the vertex, intercepts, and the direction of the curve to understand its behavior fully.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Analysis
Quadratic Functions

Formulas

y = f(x)

Theorems

Graphical Analysis Theorem

Suitable Grade Level

Grades 9-10