Math Problem Statement

Find the value of f(-2) from the graph of the piecewise function y = f(x).

Solution

The graph shows a piecewise linear function y=f(x)y = f(x). You are asked to find the value of f(2)f(-2).

To do this, we will:

  1. Locate x=2x = -2 on the x-axis.
  2. Find the corresponding y-value where the function intersects the line above or below x=2x = -2.

Upon examining the graph, when x=2x = -2, the corresponding y-value is y=2y = -2.

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

Would you like a further breakdown of this solution?

Here are 5 related questions:

  1. What is the value of f(0)f(0) based on the graph?
  2. What is the slope of the function in the region where x<0x < 0?
  3. How can we determine the equation of the line for x>0x > 0?
  4. What happens to f(x)f(x) as xx approaches 10?
  5. How does symmetry in the graph help predict values of f(x)f(x)?

Tip: To analyze graphs, always check where the function intersects the x- and y-axes as key reference points!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Graph Interpretation

Formulas

-

Theorems

-

Suitable Grade Level

Grades 6-8