## Math 1150: Precalculus, Instructor: Dana Ernst

### Review for Midterm Exam  #1

Here is a review for your upcoming test.  The test covers all of Chapter 1 (sections 1.1-1.9) and A.1, A.2, and A.3 in the Appendix.  I will not collect this.  I have provided the answers, but you should take the time to work through the problems.  The test that I give you will be very similar to this review; however, I will not limit myself to questions identical to these.  This review will give you a good indication of what you will be expected to know for the test.  Obviously, this review is longer than the exam will be.  In a couple of days, I will provide you with a list of answers for each of the following problems.

Reminders:  During the exam, SHOW ALL YOUR WORK and JUSTIFY YOUR ANSWERS when necessary.  Also, be organized and neat!

1.     Factor each polynomial completely.

(a)   Exercise 47, page 407

(b)  Exercise 51, page 407

2.     Solve the following equations.

(a)   Exercise 51, page 11

(b)

3.     Explain what  means in words and then draw it on the number line.

4.     Solve each of the following inequalities.  Give your answers in interval notation.

(a)

(b)

(c)    and

(d)  Exercise 37, page 20

(e)

(f)

5.     Exercise 71, page 20

6.     Find the distance between the points  and .

7.     Exercise 45, page 31

8.     Exercise 51, page 31

9.     Determine the slope of the line that passes through the points  and .

10.  Find the equation of the line that passes through the point  and has a slope of . Write your answer in slope-intercept form.

11.  Find the equation of the line that passes through the points  and . Write your answer in slope-intercept form.

12.  Find the equation of the line that passes through the point  and is parallel to the line .  Write your answer in slope-intercept form.

13.  Find the equation of the line that passes through the point  and is perpendicular to the line .  Write your answer in slope-intercept form.

14.  Draw an example of a graph that does not represent a function and explain why.

15.  Explain why  does not represent y as a function of x.  How many functions do you need to represent this equation?  Which ones?

16.  Give another example of an equation that does not represent y as a function of x.

17.  Exercise 19, page 53

18.  Exercise 37, page 53

19.   Find  for the function .

20.  Find  and  for the following function.

21.  Find the domain of the function .

22.  Exercise 87, page 54

23.  Find the difference quotient for .

24.  Exercise 159, page 104

25.  Exercise 37, page 65 (Donâ€™t plot points!)

26.  Exercise 53, page 66, what is the equation of this function?

27.  Determine if each of the following functions is odd, even, or neither.

(a)

(b)

(c)

28.  Describe the sequence of transformations that will yield the graph of each of the following functions relative to the associated basic function, and then sketch the graph.

(a)    relative to

(b)   relative to

(c)    relative to

(d)   relative to

29.  Write down the equation for the graph of the function that results from shifting the graph of  three units up and four units left.

30.  Given  and , find .

31.  Given  and , find .

32.  Given  and , find .

33.  Given  and , find .

34.  Given  and , find .

35.  Find functions f and g such that , where .

36.  Exercise 57, page 97

37.  Exercise 66, page 98

38.  Find the inverse of each of the following functions, if it exists.

(a)

(b)