Answer:
Pretty sure it would be the last one.
Not sure if you want me to do the work. All I can say is that it would be<em> very long.</em>
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!
Answer:the answer to this is 9
Step-by-step explanation:
Answer:
10.53
Step-by-step explanation:
Given :
Height of building = 17m
John's eye level = 2 m
Total height (including eye level) = 17+2 = 19m
Angle of depression, θ = 61°
Let distance between John's friend and building = d
Using trigonometry :
Tan θ = opposite / Adjacent
Tan 61° = 19 / d
1.8040477 = 19 / d
d = 19 / 1.8040477
d = 10.53
His error is in step 3. The variable x is being multiplied by -7 and therefore he should have divided both sides by -7, not 7 as he did.
