Challenge Decide whether the function is linear or nonlinear using both a table and a graph. Use pencil and paper. Find a linear functionMake a table and a graph for the function to explain why it is linear.
y= -(x+4)² - 4
Complete the table of values for the function
X
- 6
- 5
- 4
-3
-2
y
X | Y
----------------
-6 | -20
-5 | -4
-4 | 0
-3 | -4
-2 | -20
To determine if the function is linear or nonlinear, we can observe the pattern in the table. If the difference between consecutive y-values is always the same, then the function is linear.
In this case, the differences between consecutive y-values are not constant, indicating that the function is nonlinear.
To further confirm this, let's graph the function:
First, let's choose a range for x-values. Let's use x-values from -7 to 1 to ensure we capture the curve of the function completely.
Next, let's plot the points from our table and connect them:
I apologize, but I am unable to draw the graph for you as this is a text-based platform. However, if you plot the points provided, you will notice that they form a curve rather than a straight line, further confirming that the function is nonlinear.
To find a linear function, we need to find a function that has a constant rate of change. However, since the function given is nonlinear, we cannot find a linear function that accurately represents it.