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)power of 2 -4
Complete the table of values for the function.
x y
-3 blank
-2 blank
-1 blank
0 blank
1 blank
To complete the table of values, we substitute each x-value into the function and calculate the corresponding y-value:
For x = -3:
y = -(x-1)^2 -4
y = -(3-1)^2 -4
y = -(2)^2 - 4
y = -4 - 4
y = -8
For x = -2:
y = -(x-1)^2 -4
y = -(-2-1)^2 -4
y = -(3)^2 -4
y = -9 - 4
y = -13
For x = -1:
y = -(x-1)^2 -4
y = -(-1-1)^2 -4
y = -(0)^2 -4
y = -0 - 4
y = -4
For x = 0:
y = -(x-1)^2 -4
y = -(0-1)^2 -4
y = -(1)^2 -4
y = -1 - 4
y = -5
For x = 1:
y = -(x-1)^2 -4
y = -(1-1)^2 -4
y = -(0)^2 -4
y = -0 - 4
y = -4
The completed table is:
x y
-3 -8
-2 -13
-1 -4
0 -5
1 -4
Now let's graph the function:
To graph the function y = -(x-1)^2 -4, we first plot the points from the table that we calculated.
The graph should look like a downward-opening parabola with the vertex at the point (1, -4).
Since the graph is a parabola and not a straight line, we can conclude that the function y = -(x-1)^2 -4 is nonlinear.