Question 187707: 8. Evaluate each of the functions below at x = 1, 2, 4, 8, and 16. Plot the graph of each function. Classify each as linear, quadratic, polynomial, exponential, or logarithmic, and explain the reasons for your classifications. Compare how quickly each function increases, based on the evaluations and graphs, and rank the functions from fastest to slowest growing.
- f(x) = x^3 - 3x^2 - 2x + 1
- f(x) = e^x
- f(x) = 3x - 2
- f(x) = log x
- f(x) = x^2 - 5x + 6
my brain just dissolved. this is way to hard for me. can you do this so I can attempt to understand HOW to do this kind of problem? Thank you with all my heart. Thank you. Gabriel.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Evaluate each of the functions below at x = 1, 2, 4, 8, and 16. Plot the graph of each function. Classify each as linear, quadratic, polynomial, exponential, or logarithmic, and explain the reasons for your classifications. Compare how quickly each function increases, based on the evaluations and graphs, and rank the functions from fastest to slowest growing.
- f(x) = x^3 - 3x^2 - 2x + 1
This is polynomial, or cubic. Cubic is 3rd order, an exponent of 3.
- f(x) = e^x
This is exponential - x is in the exponent.
- f(x) = 3x - 2
This is linear. The exponent is 1. Linear is from "line" - the graph is a straight line.
- f(x) = log x
This is logarithmic. It says 'log', hard to miss.
- f(x) = x^2 - 5x + 6
This is quadratic, or 2nd order. "Quad" sounds like 4, but it refers to a square, like a quadrangle.
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To do the graphs, dl the (free) software at http://www.padowan.dk.com/graph/
It will make nice graphs that you can print, and it will evaluate the functions at the points you want.
The growth rates can be seen on the graphs.
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