How do I find the intercepts of a graph with a modulus in the equation?

  • Thread starter weedannycool
  • Start date
In summary, to find where a graph crosses the x and y axis, you need to consider two cases. If the modulus (absolute value) is always positive, the graph will be a straight line passing through (0,0). However, if the modulus is never negative, then the graph will have two x-intercepts at x=-2 and x=0, and a y-intercept at y=0.
  • #1
weedannycool
35
0
if i have an equation of a graph and it had a modulus in it. how do i find where it crosses the x and y axis. From what i know inside the modulus is alway positive.

y=|x+1|-1
 
Physics news on Phys.org
  • #2


If "inside the modulus is alway positive", that is, if x+ 1> 0, then |x+ 1|= x+ 1 and so your equation becomes y= x+ 1- 1= x. The graph of y= x is the straight line passing through (0, 0).

If, however, you only meant that the modulus (absolute value) is never negative (it can be 0), then you need to break the problem into two parts: If x< -1, then x+1< 0 and so |x+ 1|= -(x+1). For x< -1, y= |x+1|- 1= -x- 1- 1= -x- 2. That crosses the x-axis when -x- 2= 0 or when x= -2 which is less that -1 so one x-intercept is at x= -2. The "y- intercept" occurs when x= 0 which does not satisfy x< -1.

If [itex]x\ge -1[/itex] then [itex]x+ 1\ge 0[/itex] and so |x+ 1|= x+ 1. NOW we have y= |x+1|- 1= x+ 1=1 = x which crosses the x-axis and y-axis at (0,0).

The x-intercepts are x= -2 and x= 0 and the y-intercept is y= 0.
 
  • #3


thank you. i was meaning that the abosolute value is never negative.

great help.
 

FAQ: How do I find the intercepts of a graph with a modulus in the equation?

What is the equation Y = |x+1|-1?

The equation Y = |x+1|-1 is a mathematical expression that represents a function with a variable x and a constant value of 1. The function involves the absolute value of the quantity (x+1) and subtracts 1 from that value to obtain the final output, Y. This equation can be graphed as a V-shaped curve with the lowest point at (0,-1) and the highest point at (-2,1) and (2,1).

What does the absolute value in Y = |x+1|-1 mean?

The absolute value in Y = |x+1|-1 means that regardless of the value of x, the result will always be a positive number. The absolute value function removes any negative sign from a number, so the output will never be negative. In this equation, the absolute value is applied to the quantity (x+1), so the output will always be positive or 0.

Can Y = |x+1|-1 have multiple solutions?

No, Y = |x+1|-1 only has one solution for each value of x. The absolute value function always returns a single value, so when applied to the quantity (x+1) and then subtracted by 1, the result will be a single number. However, different values of x will result in different outputs, so the graph of this equation will have multiple points.

What is the domain and range of Y = |x+1|-1?

The domain of Y = |x+1|-1 is all real numbers, because any value of x can be plugged into the equation. However, the range is limited to y ≥ -1, since the lowest possible output is -1 and the absolute value function will always produce a positive value. The range does not have an upper bound, so the graph of this equation extends indefinitely upwards.

How is Y = |x+1|-1 useful in real life?

Y = |x+1|-1 can be useful in real life for various applications. For example, it can be used to calculate the distance between two points on a number line. The absolute value function removes any negative sign, so when applied to the difference between two points, it gives the absolute distance between them. This equation can also be used in physics to calculate displacement, velocity, and acceleration. In economics, it can be used to calculate profit or loss. Overall, Y = |x+1|-1 has many real-life applications in various fields.

Similar threads

Replies
5
Views
806
Replies
4
Views
1K
Replies
3
Views
1K
Replies
4
Views
6K
Replies
5
Views
2K
Replies
2
Views
1K
Back
Top