Question

f(x) = 2x^2-8/x^2-9



f(x) = 2x^2-8/x^2-9



@Mathematics

Answer 1

Showing your work at each step, analyze the graph of the following function by completing the following parts:

a. Determine the x- and y-intercepts of the graph. Write them as points.

b. Determine the domain and vertical asymptotes, if any, of the function.

c. Write the domain in interval notation.

d. Determine the horizontal or oblique asymptote, if any, of the function.

e. Obtain additional points on the graph. You should use a table (like those in the textbook or online notes) to show your work in finding the additional points.

f. Plot the x- and y-intercepts, the additional points, and the asymptotes that you found on a rectangular coordinate system and graph the function. Draw the asymptotes using dashed lines. Submit your graph in the Dropbox.

Answer 2

y = 2x^2-8/x^2-9

2x^2-8/x^2-9 = 0
2x^2-8 = 0
x^2 = 4
x = -2, 2 the x-intercepts

(-2,0) and (2,0)

y intercepts are when x = 0
i e
-8/-9 = 8/9

(0,8/9)

Answer 3

vertical asymnptotes are at x = -3 and x = 3
domain is all real values of x except -3,3

Answer 4

(-inf,+inf, x not- 3,-3)

Answer 5

limit as x --> INF y ---> 2
horizontal asymptote at y = 2

Answer 6

differentiate
-20x = 0
---
(x^2-9)^2

turning point at x = 0 , y = 8/9
second derivative -s -20 so this is a maximum

maximum at (0,8/9)

Answer 7

you now have enough points to sketch the graph
but you could plot another two
say at x = 5 and -5

Answer 8

i used the quoitent rule to differentiate

if y = f(x)/g(x, ) dy/dx = [ g(x)f'(x) - f(x)g'(x) ] / [ (g)x] ^ 2

Answer 9

ok great. So what would the graph look like? Or How do I put this in the calculator?

Answer 10

if you have a graphical calculator use the y= screen and type in the formula
or you can use wolframalpha.com