By analyzing the asymptotes we can find the graph of the rational function. Also a graph is provided below.
We have the rational function:
f(x) = (2x)/(x^2 - 1).
First, you can see that we have two zeros on the denominator. One happens when x = 1 and the other when x = -1.
This means that the graph of this function will have two vertical asymptotes at these values. (four actually as we have one going to each end in each point).
With that description we can find the graph of the function, I will also post it so you can recognize it.
If you want to learn more about rational functions, you can read:
Answer:
Step-by-step explanation:
f(x) = 2 / (x^2 - 1) is better written as
2
f(x) = ------------------
(x - 1)(x + 1)
This is undefined at x = -1 and x = 1; there are vertical asymptotes at x = -1 and x = 1.
The y-intercept is found by letting x = 0; we get
2
f(x) = ------------------ = -2 => (0, -2)
(0 - 1)(0 + 1)
Please, next time, share the answer choices. Thank you.
Much money did
Shally have at first?
I'm curious as to how a wrong answer can be a "verified answer." What is BRAINLY's process for verification?
You can see an error in the "verified answer" here:
"Amount of money that Katherine now has = [(x/3) + 68]"
No. If X is the amount of money Katherine had, and she gave away 1/3, then she has 2/3(x). And the +68?
Shelly's dad gave that $68 to Shelly, not to Katherine.
The answer my son and I came up with was $21. We used bar models since they aren't teaching 2-variable algebra in 5th grade. But here's the logic.
We know what Katherine and Shelly collectively now have $356 ($288 + $68 from the dad).
They have equal amounts now, so they each have $178. Half of that is $89, which is significant since we need to find the value of the "thirds" that constitute Katherine's original amount. She has two of those thirds left and each of the two is worth $89 (half of what she has now). This is really where the bar model method helps to visualize, by the way.
Now we now how much Katherine gave Shelly: $89 (same value as each of the other two, equal thirds of Katherine's original amount).
If we know that the $178 Shelly has now is made up from the $89 that Katherine gave her, plus the $68 her dad gave her, plus whatever mystery amount she started with, we can do $178 - ($68 + $89) and get $21.
Let's verify this answer right here:
Katherine started with $267 and Shelly started with $21.
Katherine gave Shelly $89 (1/3) of her money.
Katherine now has $178 ($267 - $89) and Shelly now has $110 ($21 + $89).
Shelly's dad gave her another $68. Now they both have $178.
Answer:
15
Step-by-step explanation:
-225/-15 = 15
A negative divided by a negative is a positive
225/15 = 15
Answer:
15
Step-by-step explanation:
The value of expression -225 divided (-15) :
-225/-15 = 15