Math Problem Statement

Evaluate functions from graphs and tables to determine specific function values and corresponding inputs.

Solution

Let's break down the questions from the image you've uploaded:

1. Evaluating Functions from Graphs:

Part 2.a:

  • f(0)=2f(0) = 2
  • f(x)=4f(x) = 4 when x=1x = -1

Part 2.b:

  • f(1)=1f(1) = 1
  • f(x)=1f(x) = -1 when x=1x = -1

Part 2.c:

  • f(2)=0f(-2) = 0
  • f(x)=1f(x) = -1 when x=5x = -5 or x=3x = -3

2. Using the table of values:

The table shows corresponding values of xx and y=f(x)y = f(x).

Part 3.a:

  • f(3)=2f(-3) = 2 (looking at the table, when x=3x = -3, f(x)=2f(x) = 2)

Part 3.b:

  • f(8)=4f(8) = 4

Part 3.c:

  • f(x)=4f(x) = 4 when x=9x = 9 or x=8x = 8 (both give the same value f(x)=4f(x) = 4)

Would you like further details or explanations on any of these?

Here are 5 follow-up questions:

  1. How do you determine f(x)f(x) values from graphs?
  2. What is the importance of solving for multiple xx-values that give the same f(x)f(x)?
  3. Can a function have more than one yy-value for a given xx-value? Why or why not?
  4. What is the significance of the points where f(x)=0f(x) = 0?
  5. How can you predict the behavior of a function just by looking at the table?

Tip: To identify values of f(x)f(x) from a graph, locate the point where the given xx-value intersects the graph and read the corresponding yy-value (i.e., f(x)f(x)).

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Interpretation
Table of Values

Formulas

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Theorems

Function Evaluation

Suitable Grade Level

Grades 8-10