Math Problem Statement

F(x)=3x-7

Solution

The function you provided is F(x)=3x7F(x) = 3x - 7.

Key features of this linear function:

  • Slope (m): The coefficient of xx, which is 3. This means for every unit increase in xx, F(x)F(x) increases by 3.
  • Y-intercept (b): The constant term, which is -7. This is the value of F(x)F(x) when x=0x = 0, meaning the line crosses the y-axis at (0,7)(0, -7).
  • Domain: Since this is a linear function, the domain is all real numbers, (,)(-\infty, \infty).
  • Range: Similarly, the range is also all real numbers, (,)(-\infty, \infty).

Would you like a more detailed explanation or visualization?

Here are some related questions:

  1. What is the slope-intercept form of a linear equation?
  2. How do you find the x-intercept of F(x)=3x7F(x) = 3x - 7?
  3. Can you find the inverse of the function F(x)F(x)?
  4. How do you graph the function F(x)=3x7F(x) = 3x - 7?
  5. What are the properties of a linear function?

Tip: The slope of a linear function determines its steepness; a larger slope means a steeper line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

Slope-intercept form: F(x) = mx + b

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 6-8