Answer:
y = x² + 6x + 8
Step-by-step explanation:
The zeros ( x- intercepts ) of the graph are x = - 4 and x = - 2, thus
the factors are (x + 4) and (x + 2) and the function is the product of the factors.
y = a(x + 4)(x + 2) ← a is a multiplier
To find a substitute (0, 8 ) the y- intercept into the equation
8 = a(0 + 4)(0 + 2) = a(4)(2) = 8a ( divide both sides by 8 )
a = 1, thus
y = (x + 4)(x + 2) ← expand using FOIL
= x² + 6x + 8
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)
<h2>
Hello!</h2>
The answer is: True.
<h2>Why?</h2>
A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.
So:
Then, evaluating we have:
Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for 
and the answer is true.
Have a nice day!
You find volume by multiplying length times width so the answer would be 300
