Math Problem Statement
Solution
The question asks: "If point (4, 5) is on the graph of a function, which equation must be true?"
Given that the point lies on the graph of a function, this means that when , the output (or -value) of the function is 5. In functional notation, this would be written as:
Now, let's examine the choices:
- — Incorrect because it implies that when , the output is 4.
- — Incorrect because this notation doesn't apply to single-variable functions.
- — This is correct because it reflects the point on the function.
- — Incorrect for the same reason as the earlier multi-variable notation.
The correct answer is:
Would you like more details, or do you have any questions about this solution?
Here are 5 related questions to explore further:
- What does it mean for a point to lie on the graph of a function?
- How do you interpret functional notation like ?
- Can a function have more than one output for the same input? Why or why not?
- What is the difference between a single-variable and a multi-variable function?
- How can we graphically verify if a point belongs to a function?
Tip: Always remember that refers to the value of the function when the input is .
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Math Problem Analysis
Mathematical Concepts
Functions
Graphing Points
Functional Notation
Formulas
f(x) = y, where x is the input and y is the output
Theorems
Graph of a function shows the relationship between inputs (x) and outputs (y)
Suitable Grade Level
Grades 8-10