(50points!)

Thank you!!!

#1. Given the function f(x)=∛x and the new function f(x)=-2 ∛x-1 , explain how the following parameters affect the second graph:

-2

-1

#2. Please see imageTWO

#3. Please see imageTHREE

#1

The term -2 vertically stretches the graph and reflects it across the y axis

The term -1 shifts the graph down by 1 unit.

#2

The quadratic regression equation is y = 2.61x^2 - 115.27x + 1568.06 (rounded to 2 decimal places)

#3

Plug in the values

2.61(23)^2 - 115.27(23) + 1568.06 = y

2.61(529) - 115.27(23) + 1568.06 = y

1,380.69 - 2,651.21 + 1568.06 = y

297.54 = y

(note I showed work here and not in the step by step because the answer asked for work to be shown)

Also just for you to know the equation obtained in #2 is gotten just by plugging the table into desmos with desmos solving for the best fit quadratic regression equation. Just google desmos quadratic regression and it should come up with a graph set up for this.

Please ask if you have any questions.

EDIT for new answers

2.12

g(-2) = -2

g(0) = 0

g(2) = 2

g(4) = -3

g(6) = -3

Explanation: The piecewise basically says anything less than or equal to two is itself, anything greater is equal to -3.

2.13

So the top number, 15 is the maximum value for y and the most growth occurs at the halfway point of y so we plug in 15/2 for y and solve for x.

15/2 = 15/(1+4e^-0.2x) then we can multiply both sides by its reciprocal and get the same denominators which we can then remove to get

2 = 1 + 4e^-0.2x subtract 1 divide by 4

1/4 = e^-0.2x then ln both sides

ln(1/4) = ln(e^-0.2x) the -0.2x can be moved out front

ln(1/4) = -0.2xln(e)      

ln(1/4) = -0.2x(1)

ln(1/4) = -0.2x

ln(1/4)/(-0.2) = x

x = 6.93

then y is 15/2 = 7.5

So our point is (6.93, 7.5)

answer: the common difference is -0.10

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: