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:
The mass will alter with time as water is absorbed back into the crystals.
Step-by-step explanation:
Answer:
68%
Step-by-step explanation:
The mean is 32 minutes, and the standard deviation is 4 minutes.
28 is 1 standard deviation below the mean, and 36 is 1 standard deviation above the mean.
According to the empirical rule, 68% of a normal distribution is between -1 and 1 standard deviations. 95% is between -2 and 2 standard deviations. 99.5% is between -3 and 3 standard deviations.
So the answer is 68%.
X + 1 < 5
x < 5 - 1
x < 4
u basically solve it like equations except for one important rule....with inequalities, when u multiply/divide by a negative number, the inequality sign changes directions. But we didn't have to deal with that rule in this particular problem
Answer:
7 & 13
Step-by-step explanation:
Let the first number be x
2nd number = 8 less than 3 times the other
2nd number = 3x - 8
Their sum = 20
X + 3x - 8 = 20
4x -8 = 20
Collect like terms
4x = 20+8
4x = 28
Divide both sides by 4
4x/4 = 28/4
X = 7
First number = 7
2nd number = 3x - 8
= 3(7) - 8
= 21 -8
= 13.
Therefore the numbers are 7 and 13
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