The table below gives approximate values for three functions, f, g, and h. One is exponential, one is trigonometric, and one is a power function. Determine which is which and find possible formulas for each.

$x$	$-2$	$-1$	0	1	2
$f(x)$	4	2	4	6	4
$g(x)$	$20.0$	$2.5$	$0.0$	$-2.5$	$-20.0$
$h(x)$	$1.33$	$0.67$	$0.33$	$0.17$	$0.08$

Both $HCO_3^-$ and $HS^-$ are amphoteric. Write an equation to show how each substance can act as an acid and another equation to show how each can act as a base.

Write an equation to show how $\ce{HC2O4-}$ can act as an acid with $\ce{HS-}$ acting as a base.

What is the conjugate acid of

$$HSO_3^-?$$

What is its conjugate base?

Consider the endothermic reaction: $C_2H_4(g) + l_2(g) \rightleftharpoons C_2H_4I_2(g)$ lf you were trying to maximize the amount of $C_2H_4I_2$ produced, which tactic might you try? Assume that the reaction mixture reaches equilibrium. a. decreasing the react ion volume, b. removing 12 from the reaction mixture, c. raising the reaction temperature, d. adding $C_2H_4$ to the reaction mixture

Consider the reaction: $\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$ $K_P$ = 0.0611 at 2000 K. A reaction mixture initially contains a CO partial pressure of 1344 torr and a $H_2O$ partial pressure of 1766 torr at 2000 K. Calculate the equilibrium partial pressures of each of the products.

An alcohol solution consists of 5 gallons of pure water and x gallons of alcohol, x>0. Let f(x) be the ratio of the volume of alcohol to the total volume of liquid. [Note that $f(x)$ is the concentration of the alcohol in the solution.]

(a) Find a possible formula for $f(x)$.

(b) Evaluate and interpret $f(7)$ in the context of the mixture.

(c) What is the zero of $f$ ? Interpret your result in the context of the mixture.

(d) Find an equation for the horizontal asymptote of $f$. Explain its significance in the context of the mixture.

What is the long-run behavior of the functions in the following problem?

$$y=\frac{2^x+3}{x^2+5}$$

Bronze is an alloy, or mixture, of copper and tin. The alloy initially contains 3 kg copper and 9 kg tin. You add x kg of copper to this 12 kg of alloy. The concentration of copper in the alloy is a function of x :

$f(x)=$ Concentration of copper $=\frac{\text { Total amount of copper }}{\text { Total amount of alloy }}$.

(a) Find a formula for $f$ in terms of $x$, the amount of copper added.

(b) Evaluate the following expressions and explain their significance for the alloy:

(i) $f\left(\frac{1}{2}\right)$

(ii) $f(0)$

(iii) $f(-1)$

(iv) $f^{-1}\left(\frac{1}{2}\right)$

(v) $f^{-1}(0)$

(c) Graph $f(x)$ for $-5 \leq x \leq 5,-0.25 \leq y \leq 0.5$. Interpret the intercepts in the context of the alloy.

(d) Graph $f(x)$ for $-3 \leq x \leq 100,0 \leq y \leq 1$. Describe the appearance of your graph for large $x$ values. Does the appearance agree with what you expect to happen when large amounts of copper are added to the alloy?

Find a possible formula for a polynomial f that has degree 2 or less, f(1)=f(5)=0 and f(2)=−3

Find the equation of the line through the $y$-intercept of $y=x^4-3 x^5-1+x^2$ and the $x$-intercept of $y=2 x-4$.

For the following problem, find the real zeros (if any) of the polynomials.

$$y=x^4+6 x^2+9$$

Is the statement in the following problem true or false? Give an explanation for your answer.

The function $f(x)=\frac{1}{x}$ is a rational function.

The following problem give value of transformations of either y= 1 / x or y=1 / x$^2$. In each case

(a) Determine if the values are from a transformation of $y=1 / x$ or $y=1 / x^2$. Explain your reasoning.

(b) Find a possible formula for the function.