Math Problem Statement

The function f(x) is graphed on the coordinate plane. What is f(-1)?

Solution

We are asked to find f(1)f(-1) based on the graph of the function f(x)f(x).

To find f(1)f(-1):

  1. Look at the x-coordinate of -1 on the graph (along the horizontal axis).
  2. Move vertically from x=1x = -1 until you hit the graph of the function.
  3. The y-coordinate at that point will be the value of f(1)f(-1).

From the graph:

  • When x=1x = -1, the corresponding yy-coordinate is 2. Thus, f(1)=2f(-1) = 2.

Let me know if you need further clarification!

Here are five related questions to consider:

  1. How can you determine the slope of this linear function from the graph?
  2. What is the equation of the line represented by f(x)f(x)?
  3. How would you calculate f(2)f(2) using the same method?
  4. Can you predict f(x)f(x) for values outside the graph, like f(10)f(-10)?
  5. How would you determine the x-intercept from this graph?

Tip: To find values of a function from a graph, always match the x-value to its corresponding y-value on the curve or line.

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Math Problem Analysis

Mathematical Concepts

Linear functions
Coordinate plane
Graph interpretation

Formulas

y = mx + b (Equation of a line)

Theorems

Linear relationships on a graph

Suitable Grade Level

Grades 6-8