Analyze the Linear Function: Is y = 3x - 1 Increasing?

Question

Given the following function:

y=3x1 y=3x-1

Is the function increasing or decreasing?

111–1–1–1000

Video Solution

Solution Steps

00:00 Is the function increasing or decreasing?
00:04 The function equation according to the given data
00:09 The function's slope is positive according to the given data
00:12 When the function's slope is positive, the function is increasing
00:18 And this is the solution to the question

Step-by-Step Solution

To determine whether the function y=3x1 y = 3x - 1 is increasing or decreasing, we need to examine its slope. The function is in the form y=mx+b y = mx + b , where m m is the slope.

For the given function, the slope m=3 m = 3 .

  • If m>0 m > 0 , the function is increasing.
  • If m<0 m < 0 , the function is decreasing.
  • If m=0 m = 0 , the function is constant (neither increasing nor decreasing).

Since the slope m=3 m = 3 is positive, the function is increasing.

Therefore, the function y=3x1 y = 3x - 1 is increasing.

Answer

Increasing