Math Problem Statement

If point (4, 5) is on the graph of a function, which equation must be true?

Solution

The question asks: "If point (4, 5) is on the graph of a function, which equation must be true?"

Given that the point (4,5)(4, 5) lies on the graph of a function, this means that when x=4x = 4, the output (or yy-value) of the function is 5. In functional notation, this would be written as:

f(4)=5f(4) = 5

Now, let's examine the choices:

  • f(5)=4f(5) = 4 — Incorrect because it implies that when x=5x = 5, the output is 4.
  • f(5,4)=9f(5,4) = 9 — Incorrect because this notation doesn't apply to single-variable functions.
  • f(4)=5f(4) = 5 — This is correct because it reflects the point (4,5)(4, 5) on the function.
  • f(5,4)=1f(5,4) = 1 — Incorrect for the same reason as the earlier multi-variable notation.

The correct answer is:

f(4)=5\boxed{f(4) = 5}

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to explore further:

  1. What does it mean for a point to lie on the graph of a function?
  2. How do you interpret functional notation like f(x)f(x)?
  3. Can a function have more than one output for the same input? Why or why not?
  4. What is the difference between a single-variable and a multi-variable function?
  5. How can we graphically verify if a point belongs to a function?

Tip: Always remember that f(x)f(x) refers to the value of the function when the input is xx.

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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