Math Problem Statement

State the domain of the following function.

y=5x−9

Solution

The given function is y=5x9y = 5x - 9.

This is a linear function of the form y=mx+by = mx + b, where m=5m = 5 and b=9b = -9. Since linear functions are defined for all real numbers, the domain of this function is the set of all real numbers.

Domain: R\mathbb{R} (or (,)(-\infty, \infty))

Would you like more details on why the domain includes all real numbers?

Here are 5 related questions for practice:

  1. What is the range of the function y=5x9y = 5x - 9?
  2. How do you find the x-intercept of y=5x9y = 5x - 9?
  3. How do you find the slope of the line represented by y=5x9y = 5x - 9?
  4. If y=5x9y = 5x - 9, what is the value of yy when x=3x = 3?
  5. What is the graph of the function y=5x9y = 5x - 9 like?

Tip: Linear functions always have a domain of all real numbers because there's no restriction on the values that xx can take.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

y = mx + b

Theorems

Linear functions have a domain of all real numbers

Suitable Grade Level

Grades 8-10