1 / 22

Section 1.3

Section 1.3. 1. Find the Domain and Range of the function below. The domain is x  -4. The graph does not cross a vertical line at x = -4. it has a vertical asymptote at x = - 4.

etoile
Download Presentation

Section 1.3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 1.3 1. Find the Domain and Range of the function below. The domain is x  -4. The graph does not cross a vertical line at x = -4. it has a vertical asymptote at x = - 4. The range is y  0. The graph does not cross the x axis which has an equation of y = 0. it has a horizontal asymptote at y = 0.

  2. 2-3 For each function: • Evaluate the given expression at the given x value. • Find the domain of the function. • Find the range. [Hint: Use a graphing calculator] 2. At x = - 1

  3. 2-3 For each function: • Evaluate the given expression • Find the domain of the function. • [Hint: Use a graphing calculator] 3. g (x) = 4 x ; find g ( - 1/2). a. Plugging -1/2 in for x yields 4 -½ = 1/2. • Graph the function and the table will show that all x work for the domain. • OR • Note that the function does not have division or even roots so all real numbers work.

  4. 4. Solve Factor out the common factor 2 x ½ . So x = 0. x = 1 and x = - 3 BUT it contains a square rood so – 3 will not work. You can also graph this function on your calculator and find the x-intercepts – zeros.

  5. Graph the function 5.

  6. Graph the function 6. It is the absolute value function shifted 3 down and 3 to the right.

  7. 7-10 Identify each function as a polynomial, a rational function. an exponential function, a piecewise linear function, or none of these. (Don’t graph them, just identify their types) 7.

  8. 8. Polynomial or linear function.

  9. 9.

  10. 10. It is not a polynomial function because one of the exponents is not an integer.

  11. For 11-14 each function find and simplify Assume h  0. 11. f (x) = 5x 2. Step 1. f(x + h) = 5 (x + h) 2 = 5x 2 + 10 xh + 5h 2 Step 2. f(x) = 5x 2 Step 3. f(x + h) – f (x) = 10 xh + 5h 2 Step 4.

  12. 12. Step 1. f(x + h) = 7 (x + h) 2 – 3 (x + h) + 2 = 7x 2 + 14 xh + 7h 2 -3x – 3h + 2 Step 2. f(x) = 7x 2 – 3x + 2 Step 3. f(x + h) – f (x) = 14 xh + 7h 2 – 3h Step 4.

  13. 13. Step 1. f(x + h) = (x + h) 3 = x 3 + 3x 2 h + 3xh 2 + h 3 Step 2. f(x) = x 3 Step 3. f(x + h) – f (x) = 3x 2 h + 3xh 2 + h 3 Step 4.

  14. 14. Step 1. Step 2. Step 3. With a bit of arithmetic work in subtracting fractions this becomes - Step 4. We are dividing step 3 by h or multiplying by 1/h.

  15. 15. Social Science: World Population The world population (in millions) since the year 1700 is approximated by the exponential function p (x) = 522 (1.0053) x where x is the number of years since 1700 (for 0 ≤ x ≤ 200) Using a calculator, estimate the world population in the year 1750.

  16. 16. Economics: Income Tax The following function expresses an income tax • that is 10% for incomes below $5000, and otherwise is $500 plus 30% of income • in excess of $5000. • Calculate the tax on an income of $3000. • Calculate the tax on an income of $5000. • Calculate the tax in an income of $10000 • Graph the function. • For x = 5000 use f(x) = 500 + 0.30(x – 5000) • f (x) = 500 + 0.30(5000 – 5000) = $500 • c. For x = 10000 use f(x) = 500 + 0.30(x – 5000) • f (x) = 500 + 0.30(10000 – 5000) = 500 + 1500 = $2000.

  17. 16. Economics: Income Tax The following function expresses an income tax that is 10% for incomes below $5000, and otherwise is $500 plus 30% of income in excess of $5000. d. Graph the function.

  18. 17. The usual estimate that each human-year corresponds to 7 dog-years is not very accurate for young dogs, since they quickly reach adulthood. A more accurate estimate is the following function expressing dog years as 10.5 dog years per human year for the first 2 years , and then 4 dog years per human years for each year thereafter: In parts a & b, 8 months is 2/3 years and 1 year and 4 months is 4/3 years.

  19. 17. The usual estimate that each human-year corresponds to 7 dog-years is not very accurate for young dogs, since they quickly reach adulthood. A more accurate estimate is the following function expressing dog years as 10.5 dog years per human year for the first 2 years , and then 4 dog years per human years for each year thereafter: c. d.

  20. 17. Conti e.

  21. 18. BONUS HOMEWORK! Business: Insurance Reserves: An insurance company keeps reserves (money to pay claims) of R (v) = 2v 0.3 , where v is the value of all if its policies, and the value of it’s policies is predicted to be v (t) = 60 + 3t, where t is the number of years from now. (Both R and v are in the millions of dollars.) Express the reserves R as a function of t, and evaluate the function at t=10.

  22. 19. Biomedical: Cell Growth One leukemic cell in an otherwise healthy mouse • will divide into two cells every 12 hours, so that after x days the number of leukemic • cells will be f (x) = 4 x . • Find the appropriate number of leukemic cells after 10 days. • If the mouse will die when its body has a billion leukemic cells, will it survive beyond day 15?

More Related