Expert: Steve Holleran - 2/18/2008

Question
Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x.

f(x) = 3x + 2
f(x) = x2 + 5x + 6
f(x) = x3 + 3x2 + 2x + 1
f(x) = ex
f(x) = log x


Answer
Hi Natrice,

Well, for the evaluation part, just make a table up listing the x-values and the results when you put them in each function, like:

 x    3x+2  x^2+5x+6  x^3+3x^2+2x+1  e^x  log x

 1      5       12         7          2.7    0

 2      8       20          25         7.4    0.301

 4      14

 8

 16

I've done the first two rows for you.

Some things you should notice:

The linear function increases at a constant rate;

The quadratic increases at an increasing rate;

The cubic at an even more increasing rate;

The exponential at an alarmingly increasing rate;

The logarithmic at a slow rate which slows even more as you increase x.

I hope this is what you needed.

Steve