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-2)squared+3
x y
0 blank
1 blank
2 blank
3 blank
4 blank
To determine if the function is linear or nonlinear using a table, we can input different values of x and see if the corresponding y values have a consistent pattern:
x y
0 3
1 2
2 3
3 6
4 11
From the table, we can observe that the y values do not have a consistent difference. Therefore, the function is non-linear.
To confirm this visually, let's plot the graph of the function.
First, let's substitute some values for x into the equation to find the corresponding y values.
When x = 0, y = -(0-2)^2 + 3 = -4 + 3 = -1.
When x = 1, y = -(1-2)^2 + 3 = -1 + 3 = 2.
When x = 2, y = -(2-2)^2 + 3 = -0 + 3 = 3.
When x = 3, y = -(3-2)^2 + 3 = -1 + 3 = 2.
When x = 4, y = -(4-2)^2 + 3 = -4 + 3 = -1.
Plotting these points on a graph, we get:
(0, -1)
(1, 2)
(2, 3)
(3, 2)
(4, -1)
Upon graphing the points, we observe that the graph does not form a straight line. Therefore, the function is non-linear.
Since the function is nonlinear, we cannot find a linear function to represent it.