Here is the problem ... p(x) = x^2 - 9x + 14 . q(x) = x^2 - 5x - 14 . f(x) = [p(x)]/[q(x)] .?

Question

p(x) = x^2 - 9x + 14 . q(x) = x^2 - 5x - 14 .
f(x) = [p(x)]/[q(x)] .


Each has two solutions.

1. There is a removable discontinuity where x = none of these

a.) none of these b.) -2 c.) 2 d.) 7

2. There is a non-removable discontinuity where x = -2

a.) none of these b.) -2 c.) 2 d.) 7

3. A zero for f(x) occurs where x = 2

a.) none of these b.) -2 c.) 2 d.) 7

4. The graph of y = f(x) has the horizontal asymptote y = 7

a.) none of these b.) -2 c.) 2 d.) 7

Answer 1

p(x) = x^2 - 9x + 14 also (x^2-9x+81/4+14-81/4) = (x-9/2)^2 + (56-81)/4 = (x-9/2)^2 - 25/4 also (x-9/2-5/2)( x-9/2+5/2) => p(x) = (x-7)(x-2)
q(x) = x^2 - 5x - 14 also (x^2-5x+25/4-14-25/4) = (x-5/2)^2 - (56+25)/4 = (x-9/2)^2 - 81/4 also (x-5/2-9/2)( x-5/2+9/2) => q(x) = (x-7)(x+2)
so f(x) = [ (x-7)(x-2) ] / [ (x-7)(x+2) ]
1. (x-7) is above and below so 7 is a removable discontinuty
2. (x+2) is only found below so -2 is a non-removable discontinuity
3. (x-2) is above and not below, so 2 is a root for f(x), i.e. f(x)=0 when x=2
4. you need to do more calculation for this one. let us do the division
f(x) = [ (x-7)(x-2) ] / [ (x-7)(x+2) ] = (x-2) / (x+2) = (x+2-4) / (x+2) = 1 - 4/(x+2)
the horizontal asimptote is for y=1

Answer 2

Well, the equation can be simplified:

p(x) = (x-2)(x-7)
q(x) = (x+2)(x-7)

p(x)/q(x) = (x-2)/(x+2)

1) d
2) True (I guess b)
3) True (c)
4) a (there is no horizontal asymptote, the graph approaches y=x)

I don't know what is meant by "Each has two solution"

Answer 3

basically x is not equal to 2.......