Math Problem Statement

f(a) = |a| + 2 a f(a) 5 10 15 20

Solution

Let's calculate the function values for f(a)=a+2f(a) = |a| + 2.

Given values of aa:

  1. a=5a = 5
    f(5)=5+2=5+2=7f(5) = |5| + 2 = 5 + 2 = 7
  2. a=10a = 10
    f(10)=10+2=10+2=12f(10) = |10| + 2 = 10 + 2 = 12
  3. a=15a = 15
    f(15)=15+2=15+2=17f(15) = |15| + 2 = 15 + 2 = 17
  4. a=20a = 20
    f(20)=20+2=20+2=22f(20) = |20| + 2 = 20 + 2 = 22

Completed Table:

aaf(a)f(a)
57
1012
1517
2022

Would you like a graph or a step-by-step breakdown of the calculations?

Related Questions:

  1. What happens to f(a)f(a) if aa is negative?
  2. How does the function f(a)=a+2f(a) = |a| + 2 compare to f(a)=a2f(a) = |a| - 2?
  3. What is the domain and range of f(a)f(a)?
  4. How does f(a)f(a) change if we modify it to f(a)=a3+2f(a) = |a - 3| + 2?
  5. Can we write this function as a piecewise function?

Tip:

Absolute value functions create V-shaped graphs because they reflect negative inputs to positive values.

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Math Problem Analysis

Mathematical Concepts

Absolute Value Functions
Function Evaluation

Formulas

f(a) = |a| + 2

Theorems

Properties of absolute value

Suitable Grade Level

Grades 6-8