Hey there! :)
Answer:
First option: As x⇒ ∞ f(x) ⇒ -∞. As x⇒ -∞ f(x) ⇒ ∞.
Step-by-step explanation:
Rearrange the equation:
f(x) = -x³ - 2x² + 1
This is a negative cubic function. The function decreases over the interval
(-∞, ∞). Therefore:
As x⇒ ∞ f(x) ⇒ -∞.
As x⇒ -∞ f(x) ⇒ ∞.
This is the first option.
Honestly this problem you can use both x and y but x tends to be the easier one to use and i would use the first equation because it is easier to solve because all the numbers are even.<span />
Answer:
The base of the ladder is 2.58 m.
Step-by-step explanation:
Given that,
The angle of elevation for a ladder from the ground is 75°.
The length of a ladder, H = 10 foot
We need to find the distance from the house should you place the base of the latter. Let the base of the ladder is b. Using trigonometry,

So, the base of the ladder is 2.58 m.
Answers:
Vertical asymptote: x = 0
Horizontal asymptote: None
Slant asymptote: (1/3)x - 4
<u>Explanation:</u>
d(x) = 
= 
Discontinuities: (terms that cancel out from numerator and denominator):
Nothing cancels so there are NO discontinuities.
Vertical asymptote (denominator cannot equal zero):
3x ≠ 0
<u>÷3</u> <u>÷3 </u>
x ≠ 0
So asymptote is to be drawn at x = 0
Horizontal asymptote (evaluate degree of numerator and denominator):
degree of numerator (2) > degree of denominator (1)
so there is NO horizontal asymptote but slant (oblique) must be calculated.
Slant (Oblique) Asymptote (divide numerator by denominator):
- <u>(1/3)x - 4 </u>
- 3x) x² - 12x + 20
- <u>x² </u>
- -12x
- <u>-12x </u>
- 20 (stop! because there is no "x")
So, slant asymptote is to be drawn at (1/3)x - 4