Question

A function is defined as y = 3x + 5 with a domain of all real numbers greater than or equal to 5.

What would be the range of the function?
A All real numbers
B All real numbers less than 20
C All real numbers greater than or equal to 20
D {20, 23, 26, 29, 32,...}

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]}