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

2007-06-16 10:55:26 · 6 answers · asked by Anonymous in Science & Mathematics Mathematics

6 answers

Well, I can't do all of this in this answer box. For example, the plotting you will have to do yourself or with a graphing calculator or some sort of graphing software. But I can nevertheless help you with this problem.

Step 1: Evaluating any function is really a very simple thing to do. You only need to plug in this value instead of the dependent variable x in your function and calculate what the value of the function is at this point. For example, if you were to evaluate the first function for x = 2, then you would get
f(4) = 2^3 - 3(4)^2-2(4) +1
= 8 - 48 - 8 + 1
= - 47

So (4, -47) is a point on the graph of this function. In fact, that's a great reason for doing the evaluation before moving on to graphing these functions...you can then plot each pair of coordinates (x, f(x)) and then draw a line of best fit through these points to finish up. So, the graphing is step 2.

Step 3:
For linear functions, the highest power of x is 1. They can be written in the form y = mx + b, where m and b are constants (m is the slope of the line and b is the y-intercept). This excludes all the functions except number 3, f(x) = 3x - 2.

For quadratic functions, the highest power of x is 2. They can be written in the form y = ax^2 + bx + c, where a, b, and c are constants. The only quadratic given is f(x) = x^2 - 5x + 6.

Polynomial functions are any functions where the only operations used are multiplication and addition and where there are no variables in the exponents. This is definitely not the formal definition but I'm not sure how to neatly write the formal definition of this without math notation that's outside the realm of this fieldbox). Functions 1, 3, and 5 are all polynomials. The others are not. The second, e^x, is not because it includes an irrational number, e, and has a variable in the exponent.

However, e^x is exponential. e is the exponential constant and any function in the form, f(x) = a (b)^x is exponential, where a and b are constants.

I'll bet you can guess which function is logarithmic.

Step 4:
Do your comparisons by drawing all the graphs on the same axes. Hopefully, you can use a graphing calculator for this.

Good luck!

2007-06-16 11:33:35 · answer #1 · answered by Anonymous · 1 0

Not sure what the question is. You have to plot the graphs and explain how each increases. The best way to do it is just solve each equation for the different values of x. It's easy to do if you can use Excel (it will even plot the graphs for you).

The classifying part can be done without even solving a single equation:

Function 1 is polynomial (see the link below).
Function 2 is exponential because the relationship has a number (e) being raised to a power.
Function 3 is linear because the graph will produce a straight line.
Function 4 is logarithmic (fairly obvious why).
Function 5 is quadratic.

2007-06-16 11:21:45 · answer #2 · answered by lango77 3 · 0 0

- f(x) = x3 - 3x2 - 2x + 1 polynomial
- f(x) = ex linear
- f(x) = 3x - 2 linear
- f(x) = log x logarithmic
- f(x) = x2 -5x + 6 quadratic
to find out the values ... replace x with 1 2 4 8 16 and calculate the thing urself
logarithimical grows the least then linear, quadratic, polynomial, exponential

2007-06-16 12:06:02 · answer #3 · answered by WraitH 3 · 0 1

You literally want to compare the two numbers, digit by digit. This particular problem is especially easy because all the digits are the same except the first. Take the "6" and the "4." The difference between these two numbers is 2. If you compare all of the other digits, there is exactly 0 difference between them, therefore zeroes fill out the rest of the answer which is 20,000. Do you see what I mean? The 7 and 7 match up; the 3 and 3 match up; the 3 and 3 match up; the 5 and 5 match up. The only digit that is different in each number is the first. And that difference is 2. Use this same idea to compare to numbers when more of the digits do not match up.

2016-05-17 11:17:44 · answer #4 · answered by ? 3 · 0 0

how old are you?
dont math texts have the answers in the back of the book?

2007-06-16 11:05:36 · answer #5 · answered by Anonymous · 0 2

sorry, math during the summer is against my happiness

2007-06-16 11:16:24 · answer #6 · answered by firecrackerjt 2 · 0 2

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