x 1 2 3 4 5
y -1 -3 3 -9 -17
To determine whether the function is linear or nonlinear, we can look at the table of values. If the difference in y-values is constant for each difference in x-values, then the function is linear.
In this case, looking at the table, the difference in y-values is not constant. For example, the difference between y-values for x = 2 and x = 1 is -3 - (-1) = -2, while the difference between y-values for x = 4 and x = 3 is -9 - 3 = -12. Therefore, the function is nonlinear.
To find a linear function, we need a relationship between x and y in which the difference in y-values is constant for each difference in x-values.
One example of a linear function could be: y = 2x - 1.
Here is the table of values for this linear function:
x 1 2 3 4 5
y 1 3 5 7 9
By looking at the table and graphing the linear function, we can see that the difference in y-values is constant for each difference in x-values, indicating that it is indeed a linear function.
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.
x 1 2 3 4 5
y
1 answer