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:
<u>I </u><em><u>believe </u></em><u>the answer would be A.</u>
Step-by-step explanation:
A says 6 x h is 54.
^ ^ ^
important!
6 is the number of hours.
h is how much money made per hour.
54 is the total after working 6 hours.
3c=12+8d
c=12+8d/3
c=4(3+2d)/3
Pretty sure it's A. (X times .5 equals Y)
I think you meant to say the equation is
y = 2x² - 2x + 3
Differentiate both sides with respect to x :
dy/dx = 4x - 2
At the point (3, 0), the slope of the tangent line is dy/dx(3) = 4•3 - 2 = 10. Then the normal line to the curve at (3, 0) has slope -1/10.
Using the point-slope formula, the equation of the normal line is
y - 0 = -1/10 (x - 3) ⇒ y = (3 - x)/10
