Polynomial, rational, exponential and logarithmic functions and graph

To exercise your skills, you are to perform the following using different tools available to you (e.g. Excel spreadsheet, graphing calculator, etc.) and write and explanation on your findings:

The graph of: f(x)= 0
The graph of: f(x) = a0 , where a0 ≠ 0
The graph of: f(x) = a0 + a1x , where a1 ≠ 0
For each of the three above:

What does the graph look like- describe the x placement
What is the graph function called?
Give an example of a number you could place in for the variable x, and describe the shift from the original graph. Remember to note what your value you are calculating for the variable x.

Solution Preview

The graph of: f(x) = 0
Whatever be the value of x, y will always be 0. So the graph is actually the x axis. This is a constant function. Any change in value of x does not shift the graph, as f(x) is independent of x.

See attached

The graph of: f(x) = a_0 where a_0 ≠ 0
Suppose a_0 = 1 ≠ 0 ...

Solution Summary

This solution graphs 3 functions and answers questions pertaining to x placement, calling graph functions and shifts from original graphs.

1.SOLVE A=1/2H(b1+b2) for b2
2. write 3-square root-36 in standard form Linear Functions
3.Find the slope of the line passing through the points (-2, 4) and (-3, 5).
a.1 b.-1 c.-9/5 d.-5/9
Zeros of Polynomial Functions
4.Find the zeros of P(x) = (

Please see the attached file for the fully formatted problems.
Assignment 3: Graphs of ExponentialandLogarithmicFunctions
Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer.
y = 3x
y = log3x
Plot the graphs of the following functions. Scan the g

1. An example of an exponential function is y=8^x. Convert this exponential function to a logarithmic function. Plot the graph of both the functions.
2. Graph these two functions
? An exponential function f(x)=6x-2
? A logarithmic function f(x)=log9x
3. Look at the graphical representation below and derive

Common and Natural Logarithms
1. For the exponential function ex andlogarithmic function log x, graphically show the effect if x is doubled.
The exponential function f (x) = e^x
you will also need to graph f (x) = e^(2x).
The common logarithmic function f (x) = log x
You will also need to graph f (x) = log (2x).

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer.
y = 2x
y = log2x
See attached file for full problem description.

Given the following values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form:
A linear equation in one variable
A linear equation in two variables (must have in at least 3 terms)
A quadratic equation (must have in at least 3 terms)
A polynomial function of three terms
An exponential function
A logarithmic func