Think of asy. as limiting fences to where your graph can travel. If, for example, you graph y = 1/x properly, you'll see that the graph never crosses either the x- or the y-axis. As x increases, your graph will get closer and closer to the line y=0 (which happens to be the horiz. axis), but will not cross it. Similarly, as x approaches x=0, the graph gets closer and closer to the vert. axis, x=0, but will not cross it. Do you see how the asymptotes limit where the graph can go?
Vertical asy. stem only from rational functions and correspond to x-values for which the denominator = 0. As you know, we can NOT divide by zero. Instead, we draw a vertical line thru any x-value at which the rational function is not defined.
Horiz. asy. have to do with the behavior of functions as x grows increasingly large, whether pos. or neg. Go back and re-read my earlier comments on horiz. asy. As x grows incr. large, in the positive direction, the graph of y=1/x approaches, but does not touch or cross, the horiz. asy.I will stop here and encourage you to ask questions if any of this discussion is not clear.
Answer:
Number 3 and 2
Step-by-step explanation:
you can use desmos to check ur answers
Answer:
i wish i could help! :(
Step-by-step explanation:
Answer:
(2,14)
Step-by-step explanation:
so i solved this with substitution but there are other methods to solve this!
equation 1 : y = -x + 16
equation 2 : y = x + 12
solve for y in equation 1 !!
y = -x + 16
(add x on both sides)
y + x = 16
(subtract y on both sides)
x = -y + 16
equation 1 now equals : x = -y + 16
substitute equation 1 into equation 2 :)
y = (-y + 16) + 12
(add 16 + 12)
y = -y + 28
(add y on both sides)
2y = 28
(divide 2 on both sides)
y = 14
now to solve for x you can insert y !
you can use equation 1 or equation 2 to solve for x.
i'm using equation 2 :
y = x + 12
(14) = x + 12
(subtract 12 on both sides)
x = 2
therefore, the answer is (2, 14).
hope this helps :p
