Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions. y=3-2 \cos x

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. [T] The Gompertz equation has been used to model tumor growth in the human body. Starting from one tumor cell on day 1 and assuming \(α=0.1\) and a carrying capacity of 10 million cells, how long does it take to reach “detection” stage at 5 million cells?

Suppose you take a dose of m mg of a particular medication once per day. Assume f equals the fraction of the medication that remains in your blood one day later. Just after taking another dose of medication on the second day, the amount of medication in your blood equals the sum of the second dose and the fraction of the first dose remaining in your blood, which is m+mf. Continuing in this fashion, the amount of medication in your blood just after your nth does is ${\displaystyle A_n=m+mf+\dots +m{f}^{n-1}}$. For the given values off and m, calculate ${\displaystyle A_5,A_{10},A_{30}}$, and ${\displaystyle \underset{n\to \mathrm{\infty }}{lim}{A}_n}$. Interpret the meaning of the limit ${\displaystyle \underset{n\to \mathrm{\infty }}{lim}{A}_n}$. f=0.25,m=200mg.

Sketch a graph of the function. Use transformations of functions whenever possible. ${\displaystyle f\left(x\right)=2x^2-1}$

In your earlier work in algebra, you learned how to recognize linear, exponential, and quadratic functions by the form of their symbolic rules. Geometric transformations also can be recognized by their symbolic rules. What transformation is defined by each of the following coordinate rules? ${\displaystyle a.(x,y)\to (5y,5x)b.(x,y)\to (-\frac{1}{2}x,-\frac{1}{2}y)c.(x,y)\to (4x-12,4y+8)}$

Begin with the graph of y = ln x and use transformations to sketch the graph of each of the given functions. ${\displaystyle y=\ln (2-x)}$

For ${\displaystyle y={\log }_3(x+2)}$ a. Use transformations of the graphs of ${\displaystyle y={\log }_{2}x}$ and ${\displaystyle y={\log }_{3}x}$ to graph the given functions. b. Write the domain and range in interval notation. c. Write an equation of the asymptote.

Find the limit (if it exists) and discuss the continuity of the function.
$\underset{(x,y,z)\to (-3,1,2)}{lim}\frac{\ln z}{xy-z}$