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)
Answer:
answer in in the photo with a explanation
<h2>(1)</h2><h2> =(a+b)(3c-d)</h2><h2> =a(3c-d)+b(3c-d)</h2><h2> =3ac-ad+3bc-bd</h2>
<h2>(2)</h2><h2> =(a-b)(c+2d)</h2><h2> =a(c+2d)-b(c+2d)</h2><h2> =ac+2ad-bc-2bd</h2>
<h2>(3)</h2><h2> =(a-b)(c-2d)</h2><h2> =a(c-2d)-b(c-2d)</h2><h2> =ac-2ad-bc+2bd</h2>
<h2>(4)</h2><h2> =(2a+b)(c-3d)</h2><h2> =2a(c-3d)+b(c-3d)</h2><h2> =2ac-6ad+bc-3bd</h2>
