Math Problem Statement
Complete the table of values for the functions f(x)=|x–3|–4 and g(x)=3x–5. Write your answers as whole numbers, decimals, or simplified fractions or mixed numbers. x f(x) g(x) 0 – 1 – 4 1 2 – 3 4 3 4 Based on the values in the table, where does the equation f(x)=g(x) have a solution?
Solution
Let's complete the table step by step by evaluating each function at the given values of .
Given functions:
Step 1: Compute and for each .
For :
For :
For :
For :
For :
Completed Table:
0 | -1 | -5 |
1 | -2 | -2 |
2 | -3 | 1 |
3 | -4 | 4 |
4 | -3 | 7 |
Step 2: Solve
We find that when , since:
Thus, the equation has a solution at .
Would you like a graphical explanation of this solution? Here are some related questions:
- How do you determine where two functions are equal algebraically?
- What is the geometric interpretation of ?
- Can we solve without making a table?
- How does the absolute value function affect the behavior of ?
- What happens if we extend the table to more values of ?
Tip: When comparing two functions, their intersection points give the solutions to .
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Math Problem Analysis
Mathematical Concepts
Absolute Value Functions
Linear Functions
Solving Equations
Formulas
f(x) = |x - 3| - 4
g(x) = 3x - 5
Theorems
Equality of functions
Suitable Grade Level
Grades 7-9
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