Math Problem Statement

Use the table to evaluate: f(-4), g(0), and f(2) + g(4).

Solution

Let's solve the problems step by step using the given table:

Given table:

  • xx values: 4,3,1,0,1,2,4,5-4, -3, -1, 0, 1, 2, 4, 5
  • f(x)f(x): 5,2,0,2,3,5,1,05, 2, 0, 2, -3, 5, -1, 0
  • g(x)g(x): 3,4,7,2,1,0,5,33, 4, 7, 2, -1, 0, 5, -3

Questions:

  1. f(4)f(-4)

    • From the table, when x=4x = -4, f(x)=5f(x) = 5.
    • Answer: f(4)=5f(-4) = 5.
  2. g(0)g(0)

    • From the table, when x=0x = 0, g(x)=2g(x) = 2.
    • Answer: g(0)=2g(0) = 2.
  3. f(2)+g(4)f(2) + g(4)

    • From the table:
      • When x=2x = 2, f(x)=5f(x) = 5.
      • When x=4x = 4, g(x)=5g(x) = 5.
    • Add these values: f(2)+g(4)=5+5=10f(2) + g(4) = 5 + 5 = 10.
    • Answer: f(2)+g(4)=10f(2) + g(4) = 10.

If you'd like further explanations or have any questions, let me know!

Here are 5 related questions to explore further:

  1. What is g(1)f(0)g(-1) - f(0)?
  2. Calculate f(5)g(5)f(5) \cdot g(5).
  3. What is f(4)g(2)f(4) - g(2)?
  4. Find the sum of f(3)+g(3)f(-3) + g(-3).
  5. How does g(x)g(x) change as xx increases?

Tip: Pay close attention to matching the xx-value in the table when evaluating functions.

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Math Problem Analysis

Mathematical Concepts

Function Notation
Table Interpretation
Basic Arithmetic

Formulas

f(x): Function notation represents the value of f at x.
g(x): Function notation represents the value of g at x.

Theorems

None explicitly involved, but the evaluation of functions is a basic principle of algebra.

Suitable Grade Level

Grades 6-8