1) given function
y = - 2 ^ ( -x + 2) + 1
2) domain: domain is the set of the x-values for which the function is defined.
The exponential function is defined for all the real numbers, so the domain of the given function is all the real numbers.
3) x-intercept => y = 0
=> y = - 2 ^ ( -x + 2) + 1 = 0 => 2^ ( -x + 2) = 1
=> - x + 2 = 0 => x = 2
The x-intercept is x = 0
4) y-intercept => x = 0
=> y = - 2 ^ ( -x + 2) + 1= - 2 ^ ( 0 + 2) 1 = - (2)^(2) + 1 =- 4 + 1 = - 3
=> The y-intercept is - 3
5) limit when x -> negative infinite
Lim f(x) when x -> ∞ = - ∞
6) limit when x -> infinite
Lim f(x) when x - > infinite = 1
=> asymptote = y = 1
7) range is the set of values of the fucntion: y
Given that the function is strictly decreasing from -∞ to ∞, the range is from - ∞ to less than 1
Range (-∞,1)
The product (found when multiplying both numbers together) of 12 and 8 is 96.
The sum (found when adding both numbers together) of 12 and 8 is 20.
The difference (found when subtracting the sum from the product) of 96 and 20 is 76!
Answer:
Step-by-step explanation:
Sn= -[-3(sin^2x + cos^2x)^n + In e.
sin^2x + cos^2x = 1 and ln e = 1, so
Sn = -(-3)^n + 1
When n = 8
this = -(-3)^8 + 1
What about if you use the distributive property? You could do 1(x+13) because the 1 would distribute to the x and the 13 making it x+13. Hope that is helpful.
<span>The answer is 5. The question wants you to compose the functions to get g(x) composed of f(x). Typically, when composing functions your substitute the second function into the first function in place of x. However, the function g(x) is constant at 5 since it has no x values. g(x)=5 means that g(x) is 5 at all values of x. Thus, in this case, it doesn't matter that we are doing a composition because the top-level function is g(x) and g(x) is 5 no matter what.</span>
