Question

Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or 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)=

Answer 1

Explanation:

the answer is f(x)= 100-30x

Answer 2

Linear

y = -30x + 100

Explanation:

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.

y = -30x + 100