For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (weight of car, average gas mileage)

Considering a function that describes how a particular car's gas mileage depends on its speed. An appropriate domain for this function would be a. $0$ to $100$ miles per hour. b. $0$ to $50$ miles per gallon. c. times from $0$ to $10$ minutes.

For each function, use your intuition or additional research, if necessary, to do the following.

a. Describe an appropriate domain and range for the function.

b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch.

c. Briefly discuss the validity of your graph as a model of the true function.

(price of gasoline, number of tourists in Yellowstone)

For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (price of gasoline, number of tourists in Yellowstone)

For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (blood alcohol content, reflex time) for a single person

For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (angle of cannon, horizontal distance traveled by cannonball)

For each function, use your intuition or additional research, if necessary, to do the following.

a. Describe an appropriate domain and range for the function.

b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch.

c. Briefly discuss the validity of your graph as a model of the true function.

(time, population of China), where time is measured in years after $1900$

In a survey conducted by Opinion Research, participants were asked, "If you had an 'X-rated' bachelor party, would you tell your fiance all, edit details, or say nothing?" The data on the following page are based on their results.

Construct a frequency distribution.

$$\begin{matrix} \text{Tell all} & \text{Edit details} & \text{Tell all} & \text{Edit details} & \text{Tell all}\\ \text{Edit details} & \text{Say nothing} & \text{Edit details} & \text{Tell all} & \text{Tell all}\\ \text{Tell all} & \text{Tell all} & \text{Edit details} & \text{Tell all} & \text{Say nothing}\\ \text{Edit details} & \text{Tell all} & \text{Tell all} & \text{Say nothing} & \text{Tell all}\\ \text{Tell all} & \text{Edit details} & \text{Tell all} & \text{Tell all} & \text{Say nothing}\\ \end{matrix}$$

For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (time, population of China), where time is measured in years after $1900$

Consider now a parabolic index waveguide with $n_1=1.50, n_2=1.46$, and $a=2 \mu \mathrm{m}$ operating again at $\lambda_0=0.6328 \mu \mathrm{m}$. Assuming the validity of Eq. (57) and that for discrete guided modes we must have $n_2^2<\beta^2 / k_0^2<n_1^2$, calculate the maximum value of $m$ and the total number of TE modes.

For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (time of day, traffic flow) at a busy intersection over a full day

For each function, use your intuition or additional research, if necessary, to do the following.

a. Describe an appropriate domain and range for the function.

b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch.

c. Briefly discuss the validity of your graph as a model of the true function.

(time of day, traffic flow) at a busy intersection over a full day

In each of the following situations, state whether two variables are related in a way that might be described by a function. If so, identify the independent and dependent variables.

You jump from an airplane (with a parachute) and want to know how far you have traveled at various times during your descent.

Find the probability of the given event.

Guessing the top three winners (in any order) from a group of $20$ finalists in a spelling bee