SOLUTION: State the x-coordinate of any holes in the graph of this function: f(x)= 8x^2-16x ---------- 5x^2-20 A. 0 B. 2 C. 5 D. -2 E. None of the above

Question 1028504: State the x-coordinate of any holes in the graph of this function:
f(x)= 8x^2-16x
----------
5x^2-20
A. 0
B. 2
C. 5
D. -2
E. None of the above
Found 2 solutions by macston, robertb:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
When the denominator is zero:

.
I am unsure what a "hole" means, but if that is the term your instructor used,
the graph is not continuous at 2 and -2.
.

.
The graph should actually show a gap at 2 and -2, which is not clear in rendering.
.
Sorry, best I can do .... Mac
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
E. None of the above.
One "hole" in the graph exists at x = 2. The graph is a hyperbola with horizontal asymptote y = 8/5 and vertical asymptote x = -2.
The function can be reduced to , where .
The discontinuity at x = -2 cannot be considered a "hole", because it is an essential/infinite discontinuity.
Thus, there is only one "hole" in the graph.
RELATED QUESTIONS
State the x-coordinate of any holes in the graph of this function: f(x)= (x+3)(6-x) (answered by MathLover1)
Find the x-coordinate of any holes for the following function. g(x)= x^2-4... (answered by jim_thompson5910)
SOMEONE PLEASE HELP!!!! 1. determine the equation of any vertical asymptotes of the... (answered by solver91311)
1)Given the function y=x+2/2x^2-4 what are the a)x intercept b)y intercept... (answered by lwsshak3)
Determine the values of x for any holes in the graph of: f(x)=... (answered by AnlytcPhil)
Determine the values of x for any holes in the graph of f(x)= x + 3/ x^2 + 5x +... (answered by Fombitz)
For the function f(x)=(x^4-625)/((x^2-25)(x+5)(x^2+25)) a) How do you find the holes... (answered by robertb)
Identify holes in the graph of the function.... (answered by Fombitz)
Find the indicated intercept(s) of the graph of the function. x-intercepts of f(x) =... (answered by ReadingBoosters)