Sketch one cycle of each sine curve. Assume a > 0. Write an equation for each graph. amplitude = 2 period = (pi/2)

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

Determine whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

Find the linear approximation of the function $f(x)=\sqrt{1-x}$ at $a=0$ and use it to approximate the numbers $\sqrt{0.9}$ and $\sqrt{0.99}$.

True or False. The domain and the range of the reciprocal function are the set of all real numbers.

Find the absolute value.
$|i^{500}|$

Find the least integer n such that ${\displaystyle f\left(x\right)}$ is ${\displaystyle O\left(x^n\right)}$ for each of these functions.
a) ${\displaystyle f\left(x\right)=2x^2+x^3\log x}$
b) ${\displaystyle f\left(x\right)=3x^5+{\left(\log x\right)}^4}$
c) ${\displaystyle f\left(x\right)=\frac{x^4+x^2+1}{x^4+1}}$

What is the inverse function of ${\displaystyle f\left(x\right)=x^2}$?