Heart Rate Suppose that a person's heart rate, $x$ minutes after vigorous exercise has stopped, can be modeled by

$$f(x)=\frac{4}{5}(x-10)^2+80 .$$

The output is in beats per minute, where the domain of $f$ is $0 \leq x \leq 10$. (a) Evaluate $f(0)$ and $f(2)$. Interpret the result. (b) Estimate the times when the person's heart rate was between 100 and 120 beats per minute, inclusive.

Use an end behavior diagram (the ones shown in the discussion) to describe the end behavior of the graph of each function. Do not use a calculator.

$$P(x)=2.74 x^4-3 x^2+x-2$$

Find all complex solutions of the given equation. Do not use a calculator.

$$7 x^3+x=0$$

For this exercise, consider the function $P(x)=2 x^2-6 x-8$.

Over what largest open interval is the function increasing? Over what largest open interval is it decreasing?

Determine a cubic polynomial function $f(x)$ in standard form having real coefficients with zeros of $4$ and $2 i$, such that $f(1)=-15$.

One or more zeros are given for this polynomial. Find all remaining zeros.

$P(x)=x^3-x^2-4 x-6 ; 3$ is a zero.

Solve the given problem.

A farmer has a thousand feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?

Perform operations and write the result in standard form. Do not use a calculator.

$$(-7 i)(1+i)$$

Solve the equation or inequality analytically, and support your result graphically.

$$x(3 x-1) \leq-4$$

For the given quadratic function, (a) write the function in the form $P(x)=a(x-h)^2+k$, (b) give the vertex of the parabola, and (c) graph the function. Do not use a calculator.

$$P(x)=-2 x^2+6 x$$

The table below shows the length and weight of a species of fish.

Fish Lengths and Weights

| Weight (lb) | $1.63$ | $2.52$ | $4.18$ | $6.58$ | $19.95$ | $62.86$

A commercial fishing boat catches fish of this species with an average length of 24 inches. If the total weight of their catch one day was $3.1$ tons, how many fish did they catch?

Fish species growth For many species of fish, the weight $W$ is a function of the length $L$ that can be expressed by

$$W=W(L)=k L^3 \quad k=\text { constant }$$

Suppose that for a particular species, $k=0.03$ and that for this species, the length (in centimeters) is a function of the number of years $t$ the fish has been alive and that this function is given by

$$L=L(t)=65-0.1(t-25)^2 \quad 0 \leq t \leq 25$$

Find $(W \circ L)(t)$ to express $W$ as a function of the age $t$ of the fish.

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?

Solve the given equation. For equations with real solutions, support your answers graphically.

$$x^2=16$$