Math Problem Statement
Solution
I have opened the image, which shows multiple mathematical problems related to function evaluation, using graphs, equations, and tables.
Let's break down each problem:
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: We are asked to evaluate . The value of can be found by using the graph provided. We look for the point on the graph where , and find the corresponding -value.
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Find when : This requires finding when the -value on the graph equals 4 and determining the corresponding -value.
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: For the function , the values are given in the table. We look up in the table.
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Find when : We need to find the value of that makes in the table.
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: The function is given by a formula, so we substitute into to find the value.
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Find when : This requires solving the equation for .
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: Using the table, find .
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Find when : This involves locating when the value of equals 12 in the table.
I'll now calculate these values.Here are the results for the given problems:
- (from the graph).
- when (from the graph).
- (from the table).
- when (from the table).
- (calculated from ).
- when (solved from the equation ).
- (from the table).
- when (from the table).
Would you like more details on any of these steps?
Here are some related questions to think about:
- How would you interpret the behavior of as increases?
- What kind of function might describe based on the table values?
- How would you solve for ?
- If the graph of were extended, what would be the next logical value for ?
- What is the slope of the function ?
Tip: When analyzing functions graphically, always double-check for turning points, as they can sometimes indicate maximum or minimum values.
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Math Problem Analysis
Mathematical Concepts
Function Evaluation
Graph Interpretation
Solving Equations
Using Tables
Linear Equations
Formulas
h(x) = 3x - 23
Theorems
Linear Function Evaluation
Graphical Analysis
Suitable Grade Level
Grades 8-10