Sketch a graph of f(x)={0 if x<=-1
{-x-1 if -1<x<=1
{-1 if x>1
Please help ASAP I'm struggling with this question!!! :(
you will have 3 parts:
1. y = 0 for x≤ -1
so on the x-axis, you will have a line starting at (-1,0) going to the left on the x-axis
So draw a line going to the left with an arrow at the end going left
2. y = -x - 1 , between -1 and 1
so from (-1,0) to (1,-2) draw a solid line, showing (1,-2) as a solid point
3. y = -1 , for x > 1
starting at (1,-1) and drawing that point as an open dot, draw a solid horizontal line with an arrow going to the right.
Your graph will be discontinuous at x = 1
Sure! To sketch the graph of the function f(x), we can follow these steps:
Step 1: Identify the critical points
The critical points are the points where the function changes its behavior. In this case, there are two critical points: x = -1 and x = 1.
Step 2: Determine the behavior around each critical point
For x ≤ -1, the function f(x) is equal to 0. So, we draw a horizontal line at y = 0 to the left of x = -1.
For -1 < x ≤ 1, the function f(x) is equal to -x - 1. This means that the graph will be a decreasing linear function from x = -1 to x = 1. At x = -1, the value of f(x) is 0, and at x = 1, the value of f(x) is -2.
For x > 1, the function f(x) is equal to -1. This means that the graph will be a horizontal line at y = -1 to the right of x = 1.
Step 3: Plot the graph
Now that we have determined the behavior of the function around each critical point, we can plot the graph:
- To the left of x = -1, draw a horizontal line at y = 0.
- From x = -1 to x = 1, draw a decreasing linear function.
- To the right of x = 1, draw a horizontal line at y = -1.
The resulting graph should resemble an inverted "V" shape, where the vertex is at (-1, 0) and the right and left branches extend to negative and positive infinity, respectively.
I hope this helps! Let me know if you have any further questions.