I am confused! Please help fast!!

Question

Write a rational expression with at least one x in the denominator and then analyze it using the following questions:

a. Set your expression equal to 0. Does this expression have any solutions? Why, or why not?

b. Set your expression equal to y and graph the equation on a graphing utility or on your calculator. Are there any values that x cannot be? Explain.

c. How do the numbers and variables in your equation relate to the features of the graph?

d. Identify the denominator of your expression; add 6 to the denominator only. How does the graph change?

Answer 1

If your rational expression is:

Then here is how I would answer the questions:

a) (4² + 8x)/(3x + 6) = 0 only when 4² + 8x = 0 (since the denominator cannot contribute to the expression being equal to zero). If 4² + 8x = 0, the 16 + 8x = 0 or x = -2. So, when x = -2, the expression equals zero.

b) y = (4² + 8x)/(3x + 6) looks like this:

"x" can never be -2

c) "x" represents the independent variable (the variable that you get to choose) and "y" represents the result after you plug in the value of "x" you choose. The coefficients of the "x" divided by each other are the value of the line (y = 8/3).

d) Adding six to the denominator moves the "undefined point" but does not change the rest of the graphed line.