Answer:
B) The maximum y-value of f(x) approaches 2
C) g(x) has the largest possible y-value
Step-by-step explanation:
f(x)=-5^x+2
f(x) is an exponential function.
Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞
Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→
Lim x→ -∞ f(x) = 2
Then the maximun y-value of f(x) approaches 2
g(x)=-5x^2+2
g(x) is a quadratic function. The graph is a parabola
g(x)=ax^2+bx+c
a=-5<0, the parabola opens downward and has a maximum value at
x=-b/(2a)
b=0
c=2
x=-0/2(-5)
x=0/10
x=0
The maximum value is at x=0:
g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2
The maximum value of g(x) is 2
For the first question, simply plug in the value of 3 into the polynomial question. The final answer is your volume of the hot water tub.
For the second question, you can figure out that x = -5 is not a real root because it does not touch or cross the x axis.
If it does it would be an solution.
Range:$43.25-$36.50=$6.75
Mean:$42.95+$36.50+$40.75+$38.25+$43.25=$201.7
Median:$40.75
Mode:none
The range is $6.75. The mean is $201.70. The median is $40.75. There is no mode.
