Question

What is the domain and range of `y = 3x - 5`?

Answer 1

Domain is all real numbers.
Range is all real numbers.

Explanation:

The domain is all the possible x values that are allowed.
The range is all the possible y values that are allowed.

Since this is a linear function, its graph is a straight line stretching from - infinity to infinity on both x and y axes, hence domain and range is all real numbers from - infinity to infinity.

This particular linear function (of form y = mx + c) has gradient m = 3 so slopes up to the right, and y-intercept c = - 5, an hence x-intercept 5/3.

The graph is sketched below and clearly extends indefinitely in terms of range and domain.

graph{3x-5 [-9.71, 10.29, -5.92, 4.08]}