Question

Determine if the data comes from a linear or exponential function. Then, enter the equation for the function. X= 0, 1, 2, 3, 4 and f(X)= 31, 19, 7, -5, -17

Answer 1

On this one, there is a consistent difference between the f(x) values:

    19-31 = -12

    7-19 = -12

    -5-7 = -12

    -17-(-5) = -12

Since that difference is consistent, this is a linear function.

We also know (from the table) that f(0)=31, so we can use the slope-intercept form of a line:

    f(x) = -12x +31

Note: The -12 is that constant difference from above, which is the slope.