Question

Determine whether the values in each table belong to an exponential function, a logarithmic function, or a linear function.

x y
0 1
1 2
2 4
3 16
4 32

Answer 1

a. quadratic
b. exponential
c. linear
d. logarithmic

Answer 2

1. It doesn't look linear (so it's not c) because the values don't increase linearly.
2. Logarithmic doesn't work because x = 0 is a valid answer
3. Exponential doesn't make sense because adjacent values don't have a common factor.

Answer: quadratic

Answer 3

You can determine the type of function by looking at the changes in y as you increase x. If the change in y is proportional to the change in x (i.e. if x doubles, y doubles) then it will be linear. If it's proportional to the square of the change in x, (i.e. if x doubles, y quadruples) then it will be quadratic. In exponential functions, the change between adjacent y's will increase by more and more each time, and in logarithmic functions the change in adjacent y's will decrease by less and less each time. So, the answer is quadratic.