Math Problem Statement

What is the function f(x) = x + 3 and how does it behave?

Solution

The given function is:

f(x)=x+3f(x) = x + 3

This is a linear function of the form f(x)=mx+bf(x) = mx + b, where:

  • m=1m = 1 (slope)
  • b=3b = 3 (y-intercept)

This function represents a straight line with a slope of 1, meaning it increases at a 45-degree angle. The graph of f(x)f(x) crosses the y-axis at (0,3)(0,3).

Would you like me to evaluate this function for specific values of xx, find its inverse, or explore related concepts?

Related Questions:

  1. What is the graph of f(x)=x+3f(x) = x + 3 and how does it look?
  2. How do we determine the inverse of f(x)=x+3f(x) = x + 3?
  3. What is the domain and range of f(x)f(x)?
  4. How does the function transformation affect f(x)=x+3f(x) = x + 3?
  5. How do you find the x-intercept of this function?

Tip: The slope of a function tells you how fast it increases or decreases. In this case, m=1m = 1, meaning for every unit increase in xx, f(x)f(x) increases by 1.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Function Graphing

Formulas

f(x) = mx + b (Slope-Intercept Form)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 6-9