Question

For the function f (graph attached inside), what are...

a) lim f(x)
x-> -7

b) lim f(x)
x-> -3

c) lim f(x)
x-> 0

d) lim f(x)
x-> 6-

e) lim f(x)
x-> 6+

f) vertical asymptote

please explain :) thanks!! i'm a bit confused how to interpret this graph!

Answer 1

graph! :)

Answer 2

what would you say is happening to the graph at x=-7 ?

Answer 3

it's a positive cubic parabola? i think that's what it is? not sure if i'm mixing things up haha

Answer 4

think of it as a rollercoaster, and you're on the line going towards -7, from right-to-left
where are you going to?

and coming from left-to-right, where are you ending up at?

Answer 5

you end up in the negatives? (-7, -3) ?

Answer 6

y = -3?

Answer 7

is not very clear that the graph ends up at y = -3 though

Answer 8

do you know what an asymptote is?

Answer 9

ohh :(

oops! not sure what i'm looking for exactly :/

Answer 10

the line touches the paper at the edge, indicating that it keeps on going and going, towards \(\pm \infty\)

Answer 11

ohh so for a), it's just + or - ∞ ?

because there's no obvious end point?

Answer 12

-∞ for a, it's going down on both sides of -7

Answer 13

ohh okay :)

so would b be +∞ ?

Answer 14

for...?

Answer 15

for b) haha

Answer 16

would that be correct?

Answer 17

a) negative infinity
b) positive infinity
c) positive infinity
d) negative infinity
e) positive infinity
f) x=-7, x=-3, x=0, x=6

Answer 18

ohhh okay i see it now :)

thank you!!! wasn't too sure how to read the graph but now i do :) yay!! Thanks a bunch!! :)