Math Problem Statement
Based on the values in the table, where does the equation f(x) = g(x) have a solution?
Solution
From the table provided in the image, we are tasked to determine where has a solution, given:
Table of values:
-3 | 8 | 8 |
-2 | 7 | 4 |
-1 | 6 | 2 |
0 | 5 | 1 |
1 | 6 |
Step-by-Step Solution:
-
Where :
- At : and , so they are equal at .
-
Between intervals:
- For : and . Since , there is no equality here.
- For : and . Again, .
- For : and . Still, .
-
Conclusion:
- at .
- The correct answer is .
Do you need further clarification or a deeper breakdown of the calculations?
Related Questions:
- What happens to as ?
- What happens to as ?
- How can you solve algebraically instead of using a table?
- How does compare to for ?
- Can and intersect more than once for ?
Tip:
Always analyze the behavior of the functions at extreme values (like or ) to understand their trends!
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Math Problem Analysis
Mathematical Concepts
Algebra
Piecewise Functions
Exponential Functions
Formulas
f(x) = |x| + 5
g(x) = (1/2)^x
Theorems
Equality of Functions
Exponential Decay Behavior
Suitable Grade Level
Grades 8-10