Question

Sketch the Asymptotes and graph the function of
y=5/(x-2)+3
Help an fellow math student! please!

Answer 1

the asymptote occurs when the denominator of the fraction = 0

Answer 2

so -2, -3? or is does the +3 just move the graph over?

Answer 3

What value of x makes x - 2 = 0?

Answer 4

-2

Answer 5

i mean 2

Answer 6

thats correct theres a vertical asymptote at x = 2

Answer 7

So how would i determine the graph? enter in 5/(x-2) and move it over 3

Answer 8

first think about the value of the function when x approaches infinity and negative infinity
the fraction will approach zero and the function will approach 3 , right?

Answer 9

Could you clarify for a layman? haha

Answer 10

if x is say 2 million then 5 /(x + 2) is pretty near to zero. Right?

Answer 11

- though it never reaches zero

Answer 12

- similarly for x = - 2 million
and because of the +3 that means that the function approaches 3
So there is a horizontal asymptote at y=3

Answer 13

So would the horizontal asymptote be 3?

Answer 14

haha i found it correctly then

Answer 15

y=3 yes

next thging to find is the y ntercept Put x = 0 and find value of y:

y = 5 /(0-2) + 3 = -2.5 + 3 = 0.5

so the graph cuts the y axis at y = 0.5

Answer 16

it will look something like thuis