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MATH-extremely difficult: Evaluate each of the functions below at x = 1, 2, 4, 8, and 16. Plot the gra?
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) = ex
- f(x) = 3x - 2
- f(x) = log x
- f(x) = x^2 - 5x + 6
if you can do this, I will definitely come back and get you 10 points for the best answer. Thanks.
- 1 decade agoFavorite Answer
first, let's classify each function:
-the first one is a polynomial function, because the highest exponent is greater than two (it's 3), and the function has more than three terms.
-the second one is a logarithmic function with base e and exponent x
-the third is a linear function, because there are no exponents, and it is in the form of f(x) = mx + b, where m is he slope (3) and b is the y-intercept (-2).
-the fourth is a logarithmic function with base x.
-the last is a quadratic function, because its highest exponent is 2.
The rates of growth ar as follows, from slowest to fastest:
-cubic function (polynomial function)
Here is a link to a graphing website, where you can punch in your functions and see how each of them looks on a graph
To evaluate the functions for ach value, simply replace x with that value. For example, for the first function, x = 1 would be
f(1) = 1^3 -3(1)^2 - 2(1) + 1
= 3 - 3 - 2 + 1
similarly, the value for x =16 is:
f(16) = 16^3 - 3(16)^2 - 2(16) + 1
= 4096 - 768 - 32 + 1
its just a matter of punching in values on your calculator, for all of them. All the other functions can be evaluted exactly like this one.