Drag and drop the answer into the box to identify each function as linear, exponential, or neither.​x​ 1 3 5f(x) 11 31 51​x​ 0 2 4f(x) 2 5 9

Accepted Solution

Answer:The first function is linear and the second is neither.Step-by-step explanation:A linear function has a constant rate of change.The rate of change is the slope; it is found using the formula[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Between the first two points, the slope ism = (31-11)/(3-1) = 20/2 = 10Between the next two points, the slope ism = (51-31)/(5-3) = 20/2 = 10This function has a constant slope, so the function is linear.In order for a function to be exponential, the percent change between y-values must be the same.To find the percent of change, we use the formula[tex]\text{percent of change}=\frac{\text{amount of change}}{\text{original amount}}[/tex]For the first two points, this is(5-2)/2 = 3/2 = 1.5For the next two points, this is(9-5)/5 = 4/5 = 0.8This is not the same; this means it is not an exponential function.