For many species of fish, the weight W is a function of the length x, given by $W=k x^3$, where k is a constant depending on the species. Suppose k=0.002, W is in pounds, and x is in inches, so the weight is $W(x)=0.002 x^3$.

a. Find the inverse function of this function.

b. What does the inverse function give?

c. Use the inverse function to find the length of a fish that weighs 2 pounds.

d. In the context of the application, what are the domain and range of the inverse function?

Determine algebraically whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. Confirm graphically.

$$y=2 x^2-3$$

f the fixed cost for producing a product is $3000 and the variable cost for the production is$3.30 x^2$ dollars, where x is the number of units produced, form the total cost function C(x).

Solve the inequality by using algebraic and graphical methods.

$$(x+5)^4>16$$

The function that models the percent of children ages 0–19 taking antidepressants from 2004 to 2009 is f (x) = -0.085x + 2.97, where x is the number of years after 2000.

a. Find the inverse of this function. What do the outputs of the inverse function represent?

b. Use the inverse function to find when the percentage is 2.3%.

Head lengths of brushtail possums follow a nearly normal distribution with mean 92.6 mm and standard deviation 3.6 mm. Compute the Zscores for possums with head lengths of 95.4 mm and 85.8 mm.

A farmer's main cash crop is tomatoes, and the tomato harvest begins in the month of May. The number of bushels of tomatoes harvested on the x th day of May is given by the equation $B(x)=$ $6(x+1)^{3 / 2}$. The market price in dollars of 1 bushel of tomatoes on the xth day of May is given by the formula $P(x)=8.5-0.12 x$.

a. How many bushels did the farmer harvest on May 8 ?

b. What was the market price of tomatoes on May 8 ?

c. How much was the farmer's tomato harvest worth on May 8 ?

d. Write a model for the worth W of the tomato harvest on the x th day of May.

Solve the inequality by using algebraic and graphical methods.

$$(x-3)^5<32$$

Let T(c) be the number of T-shirts that are sold when the shirts have c colors and P(c) be the price, in dollars, of a T-shirt that has c colors. Write a sentence explaining the meaning of the function $(T \cdot P)(c)$

Determine visually whether the graph is symmetric about the x-axis, the y-axis, or neither. If the graph represents a function, determine whether the function is even, odd, or neither.

If the outside temperature is $90^{\circ} \mathrm{F}$, the apparent temperature is given by $A(x)=$ $82.35+29.3 x$, where x is the humidity written as a decimal. Find the inverse of this function and use it to find the percent humidity that will give an apparent temperature of $97^{\circ}$ if the temperature is $90^{\circ} \mathrm{F}$.

Solve the inequality by using algebraic and graphical methods.

$$(x-2)^3 \geq-2$$

Suppose the function that converts from Canadian dollars to U.S. dollars is f(x)=1.0136 x, where x is the number of Canadian dollars and f(x) is the number of U.S. dollars.

a. Find the inverse function for f and interpret its meaning.

b. Use f and $f^{-1}$ to determine the money you will have if you take 500 U.S. dollars to Canada, convert them to Canadian dollars, don't spend any, and then convert them back to U.S. dollars.

Determine visually whether the graph is symmetric about the x-axis, the y-axis, or neither. If the graph represents a function, determine whether the function is even, odd, or neither.