# Math 116 - Chapter 1 & 2 Study Guide

1. Find the equation of the line that passes through the given points.
2. State the domain of the function. Three parts.
3. Given a function h, decompose it into two functions f and g. Two parts.
4. Find an equation having the given solutions. Leave your answer in factored form.
5. Given a function, evaluate it at the specified values and simplify. Three parts.
6. Determine if the equation represents y as a function of x. Three parts.
7. Solve the rational equation if possible.
8. Solve the formula for the indicated variable.
9. Given a table of values for x, f(x), and g(x), find the combination, composition, and inverse of functions. See example at bottom of this page. Eight parts.
10. Consider the graph of the function y=f(x) with the given domain and range. In each case identify the translation in English and give the domain and range of the translated function. Five parts. Look at your notes or the section 1.5 online lecture notes.
11. Solve the quadratic equation by factoring.
12. Solve the quadratic equation by extraction of roots.
13. Solve the quadratic equation by completing the square.
15. Perform the indicated operations with complex numbers and simplify. Write your answers in standard form. Four parts.
16. Know the equations and graphs of the basic functions. Constant, Linear (identity), Quadratic (squaring), Cubic, Square Root, Absolute Value, and the Greatest Integer Function. Identify the common function and the transformation of the graph; also write the formula for the graphed function. Also look at your take home exam, but that only required you to find the equation. This problem also wants you to name the basic function and describe the translation.
17. Find all solutions of the equation. Use any algebraic method, but show work. Three parts.
18. Solve the inequality and sketch on the real number line. Write your answers in interval notation. Two parts.

## Notes

• There is a one-to-one correspondence between problems on the study guide and problems on the exam. In other words, #13 on the study guide is what problem #13 on the exam will be about.
• There is a 25 point take home portion of this exam that is due the day of the regular exam.
• The in-class portion of the exam will be worth 100 points.

#### Example for #9

x 1 2 3
f(x) -1 5 1
g(x) 3 1 -1
• Find f(3): Find x=3 in the first row, then go down that column to the f(x) row to get f(3)=1.
• Find (f+g)(2). That's f(2)+g(2) = 5 + 1 = 6
• Find f(x) + 2g(x-2)|x=3. The vertical line with the x=3 at the bottom is read "evaluated when x=3" and means to go through and replace every x with a 3. So that becomes f(3) + 2g(3-2) = f(3) + 2g(1) = 1 + 2(3) = 7.
• Find f composed with g of 2. That is f [ g(2) ]. Since g(2)=1, we then find f (1), which is the final answer, -1.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total 3 3 4 3 3 3 3 3 16 10 4 4 4 4 8 10 9 6 100