F(x) = 2÷(x² - 2x - 3)
1)
Domain:
The domain is all the values for x that will produce a real number for y
Factor the denominator to find where y is not defined:
f(x) = 2÷(x² - 2x - 3)
f(x) = 2 ÷ (x-3)(x+1)
The domain is all real numbers except x=3 and x=-1
Range:
The range for y is all the values that y can take, given the domain.
The range is all real numbers, because y approaches both positive and negative infinite at different points on the graph.
The y-intercept is where x=0
y= 2 ÷ (0² - 2(0) -3)
y= 2 ÷ -3 = -2/3
The x-intercept are the points at which y=0.
Let's use the factored form again:
f(x) = 2 ÷ (x-3)(x+1)
This function has no x-intercepts. All values of X either produce a real number, or are undefined in the case of x=3 and x=-1
Horizontal Asymptotes
As X approaches inifinite, how does y behave?
f(x) = 2÷(x² - 2x - 3)
As x approaches both positive and negative infinite, the dominate term in the denominator, x², is vastly greater than 2, and thus y approaches zero.
The horizontal asymptote is zero, in both the positive and negative direction.
Again, let's consult the factored form:
2 ÷ (x-3)(x+1)
There are vertical asymptotes at both x=3 and x=-1. As x approaches these numbers, depending on whether x is a little bigger or smaller than either one, y approaches positive and negative infinite, since the denominator of the function approaches zero.
Therefore, there are both positive and negative vertical asymptotes at both x=3 and x=-1
As for the graph, we'll leave that to you and the many applications that can aid in such a task!
I wich i knew the answer to this dang it
Answer:
y=2x + 5 I think it should be
So since only 20 dollar bills and the other one is a 50
then
so we find some combos that will work
five 20's make 100
we
notice that we can only have 20's in multipules of 5 to make 100's
becauause 4 20's makes 80 and 3 20's make 60 and 2 20's make40 and none
of those add to 50 evenly to make 100's
(probably confusing but I hope you understand if you think about it)
so we have
5 20's =100
10 20's=200
15 20's=300
20
25
30
35
40
45 20's=900
50 20's=1000
so how many multiplules did we have?
10
but wait, if we havve 1000 in all 20's we still need at least one 50 so we subtract 100
900:9
answe ris 9 stacks
answer is 9 stacks or A
Answer:
B (2,-3) A (7,-8)
Step-by-step explanation:
they are just the same points but in the negative side of the x-axis
