Math 107 Written Assignment 2

Assignment

1. (4 pts) Which of these graphs are graphs of functions?        

(no explanation required.) (There may be more than one graph which represents a function.)

2. (6 pts) The minimum wage was $5.15 in 1990 and $7.25 in 2009 (Source: U.S. Dept. of Labor).  Find the average rate of change in the minimum wage from 1990 to 2009.  Express you answer using the units expressed in the problem.  Show all work.

3. (5 pts) State the center and the radius of the circle represented by the equation

                        (x - 4)² + (y + 6)² = 64

4. (7 pts) Solve the inequality -3(2+3x) ≥ 6 – (7x+4). Write the solution set in interval notation. Show work. 

5. (2 pts. each) Consider the following graph of y = f  (x). (Some of the points are plotted with using dots, for your convenience.)   (no explanations required)

 (a) State the y-intercept(s).

 (b) State the value of  f (−2).

 (c) State the domain.

(d) State the range.

6. (6 pts) Find the slope-intercept equation for the line pictured below. Show work/explanation.

7. (3 pts. each) Let f(x) = (2x – 3) / (x +5)

 (a) Calculate  f(-2)

 (b) State the domain of the function 

 (c) Find and simplify as much as possible: f(t+1) .   Show work.

8. (2 pts. each) Consider the linear equation 2x – 5y = 3.

(a) Write the linear equation in slope-intercept form.

 (b) State the value of the slope.

(c) State the y-intercept for this line.

(d) State a point on this line other than the y-intercept. 

9. (5 pts. each) Loudon County Phone Company charges a $100 activation fee plus a monthly fee of $0.05 per minute for every minute over 200 minutes each month.  (So, there is no monthly charge for 0 – 200 minutes of use per month).

    (a) Write an equation that can be used to determine a new subscriber’s first month’s phone bill, B(x), given the amount of minutes called, x.  (Assume that the subscriber will make over 200 minutes of calls)

 (b) Determine the subscriber’s first month’s bill if the total minutes used was 650. Show work.

 (c) Determine the number of minutes used if the new subscriber’s first month bill was $114.   Show work.

10. Consider the points (1,6) and (3,-2).

(a. 5 pts.) State the midpoint of the line segment with the given endpoints.

  (b. 5 pts.) Find the distance between the points. Show some work. Give theexact answer (involving a radical), simplify the radical as much as possible, and also state an approximation to three decimal places.

(c. 5 pts.) Find the slope-intercept equation of the line passing through the two given points. Show work.

 (d. 3 pts.) If a line is perpendicular to your line in part (c), what would the slope of that line be?

 (no work/explanation required)

11. Median home values in the United States have been increasing since the 1940’s according to data from the U.S. Census (https://www.census.gov/hhes/www/housing/census/historic/values.html. The following chart of shows the median U.S. home values for the years 1940 – 2000.

The regression line is y = 1481.4x – 2,850,000, where x = year and y = median home value in dollars. The value of R² is 0.9836.

(a, 3 pts.)  Use the regression line to estimate the U.S. median house value for the year 1985, to the nearest dollar.  Show some work.

(b, 3 pts.)  Use the regression line to predict the U.S. median house value for 2014, to the nearest dollar. Show some work.

(c, 3 pts.)  What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what the slope is telling us, in the context of this real-world application.

(d, 2 pts.) What is the value of the correlation coefficient, r? Also, interpret its value – Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?

12. Write an equivalent expression without negative exponents. Show work.

(a, 3 pts.) 1/(5.9)^-4

      (b, 3 pts.) A^-2/b^-8

(c, 3 pts.)  X^-9y^-17/z^-11