Find the slope, if it exists, of the line containing the pair of points (5, -1) and (5, -10).

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 $\sqrt{0.99}$.

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

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?

Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
${\displaystyle f\left(x\right)=-{(x-2)}^2-2}$
${\displaystyle f\left(x\right)={(x-2)}^2+2}$
${\displaystyle f\left(x\right)={(x-2)}^2-2}$
of ${\displaystyle f\left(x\right)=-{(x+2)}^2-2}$

Solve absolute value inequality.
$|2(x-1)+4|\le 8$

$\text{If X is uniformly distributed over }(-1,1),\text{ find (a) }P|X|>\frac{1}{2}$
(b) the density function of the random variable |X|.

Use the definition to show that each function is ${\displaystyle O\left(n^2\right).}$ O is big O notation
${\displaystyle F\left(n\right)=\ln \left(n\right)+5n^2}$