Algebra Question

please complete the entire assignment with completing all questions with the explanations and answers.

College Algebra
Name:
Exam II
Start Time:
Date:
End Time:
This exam contains 6 pages.
It is student’s responsibility to make sure all pages are included.
If your work is not consistent with my notes and lecture, I consider your
exam highly compromised.
You must attend a zoom meeting to explain your work for possible
consideration of partial credit.
1. Consider the function f (x) =
x−4
,
x+2
(a) (3 points) Find f (4). .
(a)
(b) (3 points) Find f (−2). .
(b)
(c) (3 points) Find f (0).
(c)
(d) (3 points) Solve f (x) = 1.
(d)
Page 1 of 6
College Algebra Exam 2
Total Points: 100
2. Consider f (x) = 3x − 4 and g(x) = 3x + 4, find
(a) (3 points) (f + g)(x).
(a)
(b) (3 points) (f − g)(x).
(b)
(c) (3 points) (f • g)(x).
(c)
(d) (4 points) (f ◦ g)(x).
(d)
3. Consider the function below:

|x| − 4 for x < 0 f (x) = − 32 x + 2 for x ≥ 0 Find: (a) (3 points) f (−4) (a) (b) (3 points) f (0) (b) (c) (3 points) f (3) (c) Page 2 of 6 College Algebra Exam 2 Total Points: 100 4. Consider a line segment AB with endpoints A(−5, 8) and B(1, 0). (a) (4 points) Find the distance between the two points. (a) (b) (3 points) Find the midpoint of the line segment AB. (b) (c) (3 points) Find the slope of the line segment AB. (c) 5. (6 points) Solve by the square root method: (5x + 4)2 = −36 5. 6. (6 points) Solve: |2x − 5| = |x − 11| 6. 7. (2 points) Suppose the domain for an increasing function is [−3, 6], what is the range of its inverse? 7. Page 3 of 6 College Algebra Exam 2 Total Points: 100 8. (6 points) Graph (x − 4)2 + (y + 2)2 = 16. Express its domain and range in interval notation. y x 8. 9. (5 points) Find the inverse of f (x) = √ x − 2. 9. 10. (5 points) Use the quadratic formula to solve 2x2 − 5x = 7. 10. Page 4 of 6 College Algebra Exam 2 Total Points: 100 11. Consider the graph of a function below: 3 2 1 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 (a) (2 points) Give its domain n interval notation. (a) (b) (2 points) Give its range in interval notation. (b) (c) (3 points) Find all x− intercepts, if any. (c) (d) (2 points) Find all y−intercepts, if any. (d) (e) (3 points) Move this graph 4 unit to the left, and then 2 units down, and draw the result. 3 2 1 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 Page 5 of 6 College Algebra Exam 2 Total Points: 100 12. (5 points) Shade the solution: f (x) >
2
x−2
5
y
x
13. (5 points) Divide
25i
.
3 − 4i
13.
14. (4 points) Find |6 − 8i|.
14.
Page 6 of 6
College Algebra Exam 2
Total Points: 100