# Math 121 - Exam 1 Study Guide

1. Use the table of values to evaluate the combination and composition of functions. Six parts. Look at problem 1.3.47 and review exercise 1.11.
2. Use the graph to evaluate the combination and composition of functions. Four parts. Look at problem 1.3.49.
3. Identify the translation and the new domain and range for each function. Five parts. Similar to the example worked in class or look at the lecture notes for section 1.5 from College Algebra.
4. Consider a polynomial function. Know the number of real or complex zeros, the maximum number of turns, the right hand behavior, the left hand behavior of the graph, and the y-intercept. Look at the review of polynomials on pages 43-44 and the section 3.2 lecture notes from College Algebra.
5. A sketch of a function is given. Use that graph to sketch the given transformations. Two parts. Look at problems 1.3.1-4.
6. Consider a rational function. Know whether the graph will touch or cross the x-axis, the right hand and left hand behavior (horizontal asymptotes), behavior at vertical asymptotes. Be able to make a sign chart for the function. Read the review of rational functions on pages 44-45 and the section 3.5 lecture notes from College Algebra.
7. Look at the graph and determine if the graphs is that of a function, a one-to-one function, or neither. Also determine whether the graph is symmetric to the x-axis, y-axis, origin, or none of these. Look at problem 1.3.62.
8. Give the exact value of the trigonometric expressions. Five parts. Look at problems 13-14 in appendix A.
9. A portion of a graph is given. Complete the graph so that it has the indicated symmetry. Three parts. Look at problem 1.3.59.
10. Given the value of one trigonometric function and the quadrant the angle lies in, find the values of the other five trigonometric functions. Look at problems 15-16 in appendix A.
11. Find all the values of θ in radians that satisfy the given equation. Look at problems 20-27 in appendix A.
12. Find the inverse of the function. Watch out for restrictions. Look at problems 1.5.9-15, 19-23.
13. Given the values of cos α and sin β, find the exact values of other trigonometric expressions involving α and β. You will need to know many of the formulas from appendix A. α and β are acute angles. Eleven parts. See below for some examples.

## Notes

• Most problems are similar to examples we've worked out in class.
• Problems from the book may be similar to the problems on the test, but you should not expect the questions on the test to be identical to those in the book.
• This chapter is a review of material covered in College Algebra and Trigonometry. There are lecture notes available online for College Algebra that may prove useful.

### Examples for #13

Let cos α = 2/3 and sin β = 4/7. Probably the best way to tackle this is to draw two right triangles -- one where the cos α = 2/3 and one where sin β = 2/7. Then use the Pythagorean relationship to find the missing side.

In triangle involving α, the length of the adjacent leg is 2 and the length of the hypotenuse is 3. That makes the length of the opposite leg √5.

In triangle involving β, the length of the opposite leg is 4 and the length of the hypotenuse is 7. That makes the length of the adjacent leg √33.

1. Find sin α. From the triangle involving α, the sin α = √5 / 3.
2. Find cos (π - α). π - α is in the second quadrant where the cosine is negative. So, cos (π - α) = - cos α = - 2/3.
3. Find tan (α+β). Since tan (α+β) = [ tan α + tan β] / [ 1 - tan α tan β ], we need to know tan α and tan β.
From the triangles you drew, you can see that tan α = √5 / 2 and tan β = 4 / √33.
Then tan (α+β) = [ √5 / 2 + 4 / √33 ] / [ 1 - (√5 / 2) (4 / √33) ].
Now multiply top and bottom by the LCD = 2√33 to get [ √165 + 8 ] / [ 2√33 - 4√5 ].

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 Total 12 4 15 5 4 4 8 10 3 5 4 4 22 100