M TH 163 Journal Topics -200 pts total

M TH 163 Journal Topics -200 pts total l o e 00 t at is solely dedicated to be a Math Journal. Each entry must be numbered and written at the top Ofa new page on the right side in your notebook. Explain in detail how to complete each entry listed. An exémple With Pictures may be used, if needed. Each skill must be completed and turned in on time (-1 p"'mt/daY/entr'y late.) Each entry will be graded separately (lOpts each). Each entry must be handwritten in a neat, clear, and concise manner so YOU and OTHERS can understand and read the explanation. it should be free of any and all grammatical and spelling errors. 1. Describe how to prove that a triangle is a right triangle if only given 3 points in a rectangular coordinate system. 2. True or False. in the equation of the circle x2 + y2 + 6x - 4y 4» 9 = o, the center is (3,2) and the radius ,‘5 4. Show and explain ALL of your reasoning. 3. Using a good example (a quadratic or a fraction), explain each step, of how to compute the difference quotient of a function. What is the definition of the difference quotient in your own words? 4. Explain, in your‘own words, the idea of increasing and decreasing functions. How are these intervals found in a function? 5. Explain how all the intercepts of an equation are found, explain what makes the equation is even or odd, and explain all 3 tests that are used to test the equation for symmetry algebraically. 6. Create a chart that summarizes the basic graphs and their properties listed in the library of functions make sure include a clear, labeled sketch of each one. 7. Create a summary chart of all function transformations including shifts, compressions, stretches and reflections. 8. in reference to a quadratic function, completely define, in your own words, vertex, axis ofsymmetry and intercepts. Draw a detailed sketch of a quadratic with the aforementioned labeled. 9. Given the perimeter of a rectangular field, describe how to find the dimensions of the field that would maximize the area. 10. Explain, in detail, the steps for manually graphing a polynomial function. In your description, define what each term means. 1 1. Given a rational function, explain how to find its domain. List and define the 3 types ofasymptotes and how each one is found. 12. Define,, in your own words, what, why, and when we use the Remainder and Factor theorems. Explain how and why long division and synthetic division of polynomials are used with these two theorems. 13. Describe the steps used to find all the zeros ofa polynomial function. Why are they so important? 14. What is GARY? Why is he so important to logarithm solving in this course? Review Topics ‘3 A. Describe how to add or subtract two rational algebraic expressions with unlike denominators. B. Explain how to simplify a complex fraction. C. What does FOll. stand for? When is it used? D. Explain how to solve a factorable quadratic equation. a E. Given a function, explain how to evaluate the function for a given x. F. Describe how to write the equation of a line, in slope-intercept form, of a line only given two points on that line.