Math Problem Statement

is y=5x-1 a function? if so, list the domain and range

Solution

Yes, the equation y=5x1y = 5x - 1 is a function. Specifically, it's a linear function, because for every input xx, there is exactly one output yy.

Domain:

The domain of the function refers to all possible values of xx. Since y=5x1y = 5x - 1 is a linear equation, there are no restrictions on xx; it can take any real number. Therefore, the domain is: Domain=(,)\text{Domain} = (-\infty, \infty)

Range:

The range of the function refers to all possible values of yy. As xx can take any real number, multiplying it by 5 and subtracting 1 will also produce any real number. Therefore, the range is: Range=(,)\text{Range} = (-\infty, \infty)

Would you like further details or have any questions?

Related questions:

  1. What is the slope of the function y=5x1y = 5x - 1?
  2. How do you find the yy-intercept of y=5x1y = 5x - 1?
  3. How would you graph the function y=5x1y = 5x - 1?
  4. What is the inverse of the function y=5x1y = 5x - 1?
  5. How does the function y=5x1y = 5x - 1 compare to y=5x+1y = 5x + 1?

Tip: In a linear function, the coefficient of xx is the slope, and it tells you how steep the line is.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Domain and Range

Formulas

Linear equation formula y = mx + b

Theorems

Function Definition

Suitable Grade Level

Grades 8-10