50 plus points
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. Input this table of values into Desmos to write a quadratic regression equation that best fits the data set. Hint: use y_2~ax_2^2+bx_2+c
b) Use your regression equation and estimate the y value if x is 23. Show your work.
x y
15 423
17 398
19 308
20 255
21 297
25 365
29 401

3.Given the piecewise function.

g(x)=(x if x≤[email protected] if x>2)┤

Find the g(x) values for the given x values.

4.Let f(x)=15/(1+4e^(-0.2x) )

What is the point of maximum growth rate for the logistic function f(x)? Show all work.

Round your answer to the nearest hundredth

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

answer: b.36 feet

step-by-step explanation: