Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential o
r linear, find a function that passes through the points. If the function is neither exponential nor linear, type NONE. x 1 2 3 4
f(x)70 40 10 -20
f(x)=
The table has a set of inputs with matching outputs. The behavior of the outputs will determine the type of function. The outputs appear to descend at a constant subtraction rate of -30 each time.
70 - 30 = 40
40 - 30 = 10
10 - 30 = -20
etc.
A constant addition or subtraction rate is a slope. Since the function has a slope, this is a linear function.
To write the function you'll need a slope and a y-intercept. Recall, the y-intercept is where x = 0. This is not in the table but can be found by reversing the process by adding 30 + 70 = 100.
Substitute m = -30 and b = 100 into y = mx+b for the equation.
Since this line has no gradient, it means that it's a horizontal or vertical line. We cannot substitute in the values because the gradient is 0 so this line will only be x = 6
