Question

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 - 3) ^ 2 + 3

Complete the table of values for the function. 1 y -1 2 2 3 3 4 2 5 1 Graph the function. Choose the correct graph below.

Decide whether the function is linear or nonlinear. Explain. Choose the correct answer below. OA. The function is nonlinear because the rate of change is constant and the graph of the function is a line. OB. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. OC. The function is linear because the rate of change is not constant and the graph of the function is not a line. OD. The function is linear because the rate of change is constant and the graph of the function is a line.

Answer 1

To complete the table of values for the function, we substitute the given values of x into the function and calculate the corresponding values of y:

1. When x = 1:
y = -(1 - 3)^2 + 3 = -(-2)^2 + 3 = -4 + 3 = -1

2. When x = 2:
y = -(2 - 3)^2 + 3 = -(-1)^2 + 3 = -1 + 3 = 2

3. When x = 3:
y = -(3 - 3)^2 + 3 = -(0)^2 + 3 = 0 + 3 = 3

4. When x = 4:
y = -(4 - 3)^2 + 3 = -(1)^2 + 3 = -1 + 3 = 2

5. When x = 5:
y = -(5 - 3)^2 + 3 = -(2)^2 + 3 = -4 + 3 = -1

The table of values for the function is:
x | y
--------
1 | -1
2 | 2
3 | 3
4 | 2
5 | -1

To graph the function, we plot the pairs (x, y) from the table on a coordinate plane:

x, y = (1, -1), (2, 2), (3, 3), (4, 2), (5, -1)

From the graph, it is clear that the points do not form a straight line. Therefore, the function is nonlinear.

The correct answer is OB. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line.