Collin County Community College Distance of The Planet Mercury Lab Report

1. For this lab, click on the link for the pdf file below to download the lab.

2. Complete the lab either by typing the work and answers or print the labs and write on the paper copies. If you aren’t able to print, then write the answers on blank paper. Show your work in the space provided! Please BOX and/or HIGHLIGHT your final answer. For assistance in the math when completing the lab on your computer, click on the following links to go to the indicated pages: How to Use the Math Equation Editor and How to Insert or Paste a Desmos Graph.

3. Once you have completed the problems, then submit your typed lab as a file to Canvas or scan your written copy and submit the pdf file to Canvas. Please do not upload a picture! Upload your scanned document on Canvas by clicking on “Submit Assignment.”

If you do not have access to a scanner, consider downloading the free version of a scanner app on your mobile device. These aps allow you to take a picture of a document and save it as a pdf file. Take pictures of all of the lab pages and save them as a single pdf document which you can then email to yourself and upload to Canvas. For further information, click the link to go to the page: How to Scan and Upload Submissions (in the Additional Resources for Students Module).

Math 1314
Lab Module 1
Name _____________________
For each of the following problems, show all work! Simplify and clearly indicate all answers.
7
2D can be used to approximate the speed S, in miles per hour, of a car
2
that has left skid marks of length D, in feet. How fast would a car have been traveling if it left a
skid mark that is 102.04 feet long? Round to the nearest integer. Clearly state your final answer
in a complete sentence with proper grammar and correct spelling.
1. The function S(D) =
2. For each planet in the solar system, its year is the time it takes the planet to revolve around the
3
center star. The formula E( x ) = 0.2x 2 models the number of Earth days in a planet’s year, E,
where x is the average distance of the planet from the center star, in millions of kilometers. There
are approximately 88 Earth days in the year of the planet Mercury. What is the average distance of
Mercury from the center star? Round to the nearest million kilometers. Clearly state your final
answer in a complete sentence with proper grammar and correct spelling.
Math 1314
Lab Module 1
3. For the graph g(x) below, find the indicated information. Write answers in interval
notation where appropriate.




− − − − − − −








−
−
−
−
a. Find g(5).
b. State the intervals of x where the graph is increasing.
c. State the intervals of x where the graph is decreasing.
d. State the interval of x where the graph is constant.
e. State the coordinates of the x-intercept(s).
f. State the coordinates of the y-intercept.
g. State the domain in interval notation.
h. State the range in interval notation.
i. Find any relative maxima.
j. Find any relative minima.
page 2
Math 1314
4.
Lab Module 1
page 3
Sketch the function that has a graph the shape of r(x) = x , reflected over the y-axis and
vertically stretched by a factor of 3. Write the equation of the function. State the domain of the
y
transformed function in interval notation.
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
5.
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
2
3
4
5
6
7
8
9
x
Sketch the function that has a graph the shape of s(x) = x2, with a horizontal shrink by a factor of
⅓ and shifted up two units. Write the equation of the function. State the domain of the
transformed function in interval notation.
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
x
-3
-4
-5
-6
-7
-8
-9
9
8
6. Sketch a graph of the function a(x) = ½ x + 4 .
Describe the transformations to the graph of y =
7
6
5
4
3
2
1
3
3
y
x.
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
9
8
y
7
6
5
4
3
2
1
7. Sketch a graph of the function c(x) = (½x)3 – 1.
Describe the transformations to the graph of y = x3
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
Math 1314
Lab Module 1
page 4
8. State the domain and range of the following function. Describe the transformations to the basic
function. Then, write the equations of each of the function.
9
8
y
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
9
x
-2
-3
-4
-5
-6
-7
-8
-9
9. The graph of a function p(x) is shown. Draw the graph of –p(x – 1) – 3.
8
9
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-8
-7
-6
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
-6
-7
-8
-9
y
1
2
3
4
5
6
7
8
9
-9
-8 -7
-6
-5 -4
-3
-2
-1
-1
-2
-3
-4
-5
-6
-7
-8
-9
1
2
3
4
5
6
7
8
9
x
Math 1314
10.
Lab Module 1
For the function
− 3 x + 5 if
f(x) = 
 x − 1 if
x 1
x 1
page 5
,
9
8
y
7
a. Evaluate f(–1)
6
5
4
b. Evaluate f(1)
3
2
1
c. Evaluate f(0)
-9
-8 -7
-6
-5 -4
-3
-2
-1
-1
1
2
3
4
5
6
7
8
9
x
-2
-3
d. Evaluate f(5)
-4
-5
-6
e. Graph the function.
-7
-8
-9
11. Determine algebraically whether the function is even, odd or neither:
g(x) =
x
x +3
2
______________________
Math 1314
Lab Module 1
Name _____________________
For each of the following problems, show all work! Simplify and clearly indicate all answers.
7
2D can be used to approximate the speed S, in miles per hour, of a car
2
that has left skid marks of length D, in feet. How fast would a car have been traveling if it left a
skid mark that is 102.04 feet long? Round to the nearest integer. Clearly state your final answer
in a complete sentence with proper grammar and correct spelling.
1. The function S(D) =
2. For each planet in the solar system, its year is the time it takes the planet to revolve around the
3
center star. The formula E( x ) = 0.2x 2 models the number of Earth days in a planet’s year, E,
where x is the average distance of the planet from the center star, in millions of kilometers. There
are approximately 88 Earth days in the year of the planet Mercury. What is the average distance of
Mercury from the center star? Round to the nearest million kilometers. Clearly state your final
answer in a complete sentence with proper grammar and correct spelling.
Math 1314
Lab Module 1
3. For the graph g(x) below, find the indicated information. Write answers in interval
notation where appropriate.




− − − − − − −








−
−
−
−
a. Find g(5).
b. State the intervals of x where the graph is increasing.
c. State the intervals of x where the graph is decreasing.
d. State the interval of x where the graph is constant.
e. State the coordinates of the x-intercept(s).
f. State the coordinates of the y-intercept.
g. State the domain in interval notation.
h. State the range in interval notation.
i. Find any relative maxima.
j. Find any relative minima.
page 2
Math 1314
4.
Lab Module 1
page 3
Sketch the function that has a graph the shape of r(x) = x , reflected over the y-axis and
vertically stretched by a factor of 3. Write the equation of the function. State the domain of the
y
transformed function in interval notation.
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
5.
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
2
3
4
5
6
7
8
9
x
Sketch the function that has a graph the shape of s(x) = x2, with a horizontal shrink by a factor of
⅓ and shifted up two units. Write the equation of the function. State the domain of the
transformed function in interval notation.
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
x
-3
-4
-5
-6
-7
-8
-9
9
8
6. Sketch a graph of the function a(x) = ½ x + 4 .
Describe the transformations to the graph of y =
7
6
5
4
3
2
1
3
3
y
x.
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
9
8
y
7
6
5
4
3
2
1
7. Sketch a graph of the function c(x) = (½x)3 – 1.
Describe the transformations to the graph of y = x3
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
Math 1314
Lab Module 1
page 4
8. State the domain and range of the following function. Describe the transformations to the basic
function. Then, write the equations of each of the function.
9
8
y
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
9
x
-2
-3
-4
-5
-6
-7
-8
-9
9. The graph of a function p(x) is shown. Draw the graph of –p(x – 1) – 3.
8
9
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-8
-7
-6
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
-6
-7
-8
-9
y
1
2
3
4
5
6
7
8
9
-9
-8 -7
-6
-5 -4
-3
-2
-1
-1
-2
-3
-4
-5
-6
-7
-8
-9
1
2
3
4
5
6
7
8
9
x
Math 1314
10.
Lab Module 1
For the function
− 3 x + 5 if
f(x) = 
 x − 1 if
x 1
x 1
page 5
,
9
8
y
7
a. Evaluate f(–1)
6
5
4
b. Evaluate f(1)
3
2
1
c. Evaluate f(0)
-9
-8 -7
-6
-5 -4
-3
-2
-1
-1
1
2
3
4
5
6
7
8
9
x
-2
-3
d. Evaluate f(5)
-4
-5
-6
e. Graph the function.
-7
-8
-9
11. Determine algebraically whether the function is even, odd or neither:
g(x) =
x
x +3
2
______________________