Challenge: Decide whether the function is linear or nonlinear using both a table and a graph. Use pencil and paper. Find a linear function. Make a table and a graph for the function to explain why it is linear.
y = - (x + 1)^2 - 4
x y
-3
-2
-1
0
1
To determine whether the function is linear or nonlinear, we will first complete the table and create a graph based on the provided function.
To populate the table, we substitute the given values of x into the function and solve for y:
x | y
-3 | -12
-2 | -7
-1 | -4
0 | -5
1 | -8
Now, we can plot the points from the table on a graph. The x-values represent the horizontal axis, and the y-values represent the vertical axis.
|
- + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + (x-axis)
|
- |
-7 |
|
|
- + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + - (y-axis)
|
|
-12 |
|
Looking at the graph and the table, we can conclude that the function y = - (x + 1)^2 - 4 is nonlinear.
To find a linear function, we need to look for a relationship where the change in y over a constant change in x is constant. From the table and graph, we can see that the y-values do not change linearly. Therefore, we cannot find a linear function based on the given data.