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Solve the following equation using the quadratic formula.
Evaluate the function at the given values of the independent variable and simplify.
Use the graph of f to determine each of the following.
(a) the domain of f
(b) the range of f
(c) the zero(s) of f
(d) f left parenthesis 4 right parenthesis
(e) the intervals on which f is increasing
(f) the intervals on which f is decreasing
(g) the values for which
f(x)less than or equals0
(h) any relative maxima or minima
(i) the value(s) of x for which f left parenthesis x right parenthesis equals 4
(j) Is f left parenthesis 3 right parenthesis positive or negative?
Give the slope and y-intercept of the line whose equation is given below. Then graph the linear function.
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Find the average rate of change of the function
Use the graph of y =f (x) to graph the function
Begin by graphing the absolute value function, f (x)=|x|. Then use transformations of this graph to graph the given function.
For f(x)=x+4 and g(x)=2x+1, find the following functions.
The function f (x)=x^3-6 is one-to-one. Find an equation for f-1(x), the inverse function.
Find the distance between the pair of points.
Find the midpoint of the line segment whose endpoints are given.
Use a graphing utility with a viewing rectangle large enough to show end behavior to graph the polynomial function shown below.
Use the seven step method described in the book to graph the following rational function.
The purpose of the Signature Assignment is to have you work with real-life data to answer a real-life question using the tools, technology, and skills of MTH/220. In the first week, you must develop a question that can be answered with numerical data and that spans over at least 10 years. For example, “How has the population of the world changed over the past 50 years, and when will the population be unsustainable?”
Here is a list of possible sources to find your data:
Healthcare Data
Educational Data
Criminal Data
Select type of table under Law Enforcement or Incarcerations
Select year
Then select the type of data you are looking for from the dropdown menus and click on Excel. The table will automatically download on your computer.
Mortgage Data
Census Data (Population, economy, business, education, employment, health, housing, income, trade)
UN Data (income, trade, religion, health, poverty)
Health Data
Globalization, Health, and Agriculture Data
UCR Data (crime)
You can either choose a topic from the Student Topics and Questions List or you can create your own. If you chose to create your own, you must obtain instructor approval. You may choose to find data elsewhere (if not listed above), but if you do, you must get the data approved by your instructor. It is very important the data you collect meet the following requirements:
It has data from a trusted/peer-reviewed source that is numeric per year
You can collect at least 10 data points (data over at least 10 years old)
Your question can be answered with the data.
In a Microsoft® Word document containing 30 to 45 words, write the topic/question you are addressing, where you plan to find your data (even if it is one of the above sources), and why you chose this topic. Your assignment will be graded with Week 1 Grading Guide.
Click the Assignment Files tab to submit your assignment.
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Use the graph of the rational function to complete the following statement.
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function.
Find the horizontal asymptote, if any, of the graph of the rational function.
The function models the pH level, f(x), of a mouth x minutes after eating food containing sugar. The graph of this function is shown to the right. Complete parts (a) through (e).
Graph the following function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
Use transformations of the graph of f left parenthesis x right parenthesis equals 4 Superscript x
to graph the function g(x) given below. Graph and give the equation of the asymptote. Use the graph to determine the domain and range of g(x).
Evaluate the following expression without using a calculator.
Evaluate the expression without using a calculator.
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible.
The loudness level of a sound can be expressed by comparing the sound’s intensity to the intensity of a sound barely audible to the human ear. The formula describes the loudness level of a sound, D, in decibels, where I is the intensity of the sound, in watts per meter squared,and I 0is the intensity of a sound barely audible to the human ear. Use this information to answer parts (a) and (b) below.
Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
Complete the table shown to the right for the population growth model for a certain country.
Solve the system of equations by the substitution method.
Solve the system by the addition method.
Solve the system by the method of your choice.
Four times a first number decreased by a second number is negative 38. The first number increased by twicethe second number is 4.Find the numbers.
Solve the system by the substitution method.
Graph the following inequality.
Graph the following inequality.
Graph the solution set of the system of inequalities.
Write the augmented matrix for the system of equations to the right.
Write the system of linear equations represented by the augmented matrix to the right. Use x, y, and z for the variables.
Perform the row operation on the given augmented matrix.
Solve the system using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
a. Give the order of the given matrix.
b. If A equals left bracket a Subscript ij Baseline right bracket ,identify a 32and a 23 if possible.
Find the following matrices where A= b=
Find the following matrices where.
Write the first four terms of the sequence whose general term is given below.
The sequence given is defined using a recursion formula. Write the first four terms of the sequence.
Evaluate the factorial expression.
Find the indicated sum. A deposit of $1000is made in an account that earns 5%
interest compounded quarterly. The balance in the account after n quarters is given by the following sequence. Find the balance in the account after six years.
Select the answers that best complete the given statements.
Write the first six terms of the arithmetic sequence with the given first term, a 1, and common difference, d.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term,a 1, and common difference, d.
Find 1plus2plus3plus4plus…plus30, the sum of the first 20natural numbers.
You are considering two job offers. Company A will start you at $ 33 comma 000a year and guarantee a raise of $ 2500per year. Company B will start you at a higher salary, $ 40 comma 000a year, but will only guarantee a raise of $ 1000per year. Find the total salary that each company will pay over a ten-year period. Which company pays the greater total amount?
Open the Microsoft® Excel® file you created in Week 3 with the best fit line.
Select “Save As” to create a new version of this workbook.
Delete your commentary from Week 3 and add new commentary per below:
Answer the following in 175 to 260 words in your commentary:
How does the graph of a line compare to an arithmetic sequence? What does the slope represent? How would you find the first term?
Use your best fit equation to make a formula for the nth term of an arithmetic sequence. The year will represent the number of the term, and your data value will be the value at that term.
Use your arithmetic equation to predict what the 2,050th term will be. Do you think this is a good estimate of what the real value will be? Why or why not?
Challenge Option
Open your Microsoft® Excel® file from Week 2 with your exponential graph.
Click “Save As” to create a new version of this file.
Delete the old commentary.
Answer the following by adding new commentary:
How does the graph of an exponential equation compare to a geometric sequence? How would you find the common ratio? How would you find the first term (assuming the year is the number of the term)?
Use your best fit equation to make a formula for the nth term of a geometric sequence. The year will represent the number of the term, and your data value will be the value at that term.
Use your geometric equation to predict what the 2,050th term will be. Do you think this is a good estimate of what the real value will be? Why or why not?
Save your Microsoft® Excel® file, including your old graphed equation and new commentary. Make sure you do not delete your files, as you will need them in subsequent weeks. Your assignment will be graded with the Week 4 Grading Guide.
Click the Assignment Files tab to submit your assignment.
Create a Microsoft® PowerPoint® presentation and include the following:
One slide (Introduction) on your topic and question
Which topic/question did you choose?
Why does it interest you?
Where did you find the data?
One slide for each graphic (minimum of 3 graphics)
These should be clear, neat, organized, and labeled
Explain how you created these and show your answers to the previous weeks questions in the notes section of your slide
What did you conclude in each week?
One slide for a conclusion
Restate your topic and question, and give your answer to the question.
Show which model you chose that best fits your data and explain why.
Make a prediction about a future value based on your model and equation
Save your Microsoft® PowerPoint® presentation.
Add commentary in the notes sections, not in the slide itself. The notes should be 30-45 words per slide. The commentary should be everything you would say if you were giving the Microsoft® PowerPoint® presentation in person. Your presentation will be graded using the Signature Assignment Rubric.
Click the Assignment Files tab to submit your assignment.
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Solve for x using the quadratic formula.
Evaluate the function at the given values of the independent variable and simplify.
Use the graph of f to determine each of the following.
(a) the domain of f
(b) the range of f
(c) the zero(s) of f
(d) f left parenthesis 4 right parenthesis
(e) the intervals on which f is increasing
(f) the intervals on which f is decreasing
(g) the values for which
f(x)less than or equals0
(h) any relative maxima or minima
(i) the value(s) of x for which f left parenthesis x right parenthesis equals 4
(j) Is f left parenthesis 3 right parenthesispositive or negative?
Give the slope and y-intercept of the line whose equation is given below. Then graph the linear function.
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Find the average rate of change of the function
Use the graph of y =f (x) to graph the function
Begin by graphing the absolute value function, f (x)=|x|. Then use transformations of this graph to graph the given function.
For f(x)=x+4 and g(x)=2x+1, find the following functions.
The function f (x)=x^3+6 is one-to-one. Find an equation for f-1(x), the inverse function.
Find the midpoint of the line segment whose endpoints are given.
Use the graph of the rational function to complete the following statement.
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function.
Find the horizontal asymptote, if any, of the graph of the rational function.
The function f models the pH level, f(x), of a mouth x minutes after eating food containing sugar. The graph of this function is shown to the right. Complete parts (a) through (e).
Graph the following function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
Use transformations of the graph of f =3^x to graph the function g(x) given below. Graph and give the equation of the asymptote. Use the graph to determine the domain and range of g(x).
Evaluate the following expression without using a calculator.
Evaluate the following expression without using a calculator.
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible.
The loudness level of a sound can be expressed by comparing the sound’s intensity to the intensity of a sound barely audible to the human ear. The formula
Upper D equals 10 left parenthesis log Upper I minus log Upper I 0 right parenthesis
describes the loudness level of a sound, D, in decibels, where I is the intensity of the sound, in watts per meter squared commaand Upper I 0 is the intensity of a sound barely audible to the human ear. Use this information to answer parts (a) and (b) below.
Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
Complete the table shown to the right for the population growth model for a certain country.
Solve the system by the substitution method.
Solve the system by the addition method.
Solve the system by the method of your choice.
Use the graphs of the linear functions on the right. Write the linear system whose solution set is
{(3,negative 1)}. Express each equation in the system in slope-intercept form.
Solve the system by the substitution method.
Graph the following inequality.
Graph the given system of inequalities.
Solve the system using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
Find the following matrices where A= B=
Solve the matrix equation B-X=2A for X.
The sequence given is defined using a recursion formula. Write the first four terms of the sequence.
Evaluate the factorial expression.
Find the indicated sum.
Write the first six terms of the arithmetic sequence with the given first term, a 1, and common difference, d.
Write a formula for the general term (the nth term) of the arithmetic sequence shown below. Do not use a recursion formula. Then use the formula for An to find a20 ,the 20 th term of the sequence.
Find 1plus2plus3plus4plus…plus30, the sum of the first 30natural numbers.
Company A pays $24 comma 000yearly with raises of $1 comma 400per year. Company B pays $ 28 comma 500yearly with raises of $850 per year. Which company will pay more in year 10? How much more?
Write the first five terms of the geometric sequence whose first term is 32, and whose common ratio is
Find the sum of the first 14 terms of the geometric sequence shown below.
The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
A job pays a salary of $15 comma 000 the first year. During the next 11years, the salary increases by 7% each year. What is the total lifetime salary over the 12-year period?
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