Question

p(w)=(3w+5)/(6-2w)
do i need to solve this? or find the intercepts?

Answer 1

what's the context?

Answer 2

1. Sketch an graph of the function:
. Make sure to include the asymptotes and the intercepts, along with labels and an appropriate scale. This graph must be hand drawn.

Answer 3

ok, well, I assume you covered asymptotes already so

Answer 4

I found x=3, for vertical asymptote, and y=3w+5/2(3-w) for horizontal

Answer 5

your vertical asymptotes will occur at the roots of the denominator, when set to 0, that is

6-2w = 0

solve for "w" :) and that's your vertical asymptote

Answer 6

6-2w =0
6 = 2w
3 = w

thus yes, your vertical asymptote is at 3 :)

Answer 7

your horizontal asymptotes occur when the numerator degree is LESS or equal to that of the denominator's
if it's LESS then the horizontal asymptote occurs at the x-axis, that is y=0

if both numerator's and denominator's degree are the same, then your vertical asymptote occurs at \(\bf \cfrac{\text{leading coefficient}}{\text{leading coefficient}}\)

Answer 8

yay! the rest though.. would the x intercept be at 3? and y?

Answer 9

so y=7?

Answer 10

as usual, when the function touches the x-axis, "y" is 0
when the function touches the y-axis, "x" is 0

so set either to 0 to find the other's intercept

Answer 11

so is p(w) the same as y?

Answer 12

hmm, yes

Answer 13

what your function is using is a variable "w"
as opposed to say "x"
and p(w) as opposed to "y"
but the axis system is generic and can use whatever you want to label the axis, so long they correlate

Answer 14

you can if you want think of p(w)=(3w+5)/(6-2w) as y=(3x+5)/(6-2x)

Answer 15

yes, i get always confused when they switch the variables-why cant life be simple?- :) thank you so much for your help, i feel i know how to, but my brain is fighting to see clearly

Answer 16

so do i substitute the value of x 930 on y=(3x+5)/(6-2x) and solve, or is this not asked of me?

Answer 17

doesn't seem so, just to get those values to graph it

Answer 18

$$\bf p(w) = \cfrac{3w+5}{6-2w}\\
\text{y-intercept, x = 0}\\
p(w) = \cfrac{5}{6}\\
\text{x-intercept, p(w) = 0}\\
0 = \cfrac{3w+5}{6-2w} \implies 0 = 3w+5 \implies -\cfrac{5}{3}
$$

Answer 19

and the asymptotes are at
vertical, w = 3
horizontal, y= -3/2

Answer 20

oh... im confused by the -5/3.. ok, thanks so much, im graphing it!