Download Summer Preparation for PRECALCULUS HONORS

Summer Preparation for PRECALCULUS HONORS
This worksheet is a review of the entering objectives for Precalculus with Analysis and is due on the first day back
to school. Please show work NEATLY and on a SEPARATE sheet of paper. Have a great summer!! We are
looking forward to seeing you in August.     _Your future Precalculus Honors Teachers
In exercises 1-2, find the points that are symmetric to the given point
(a) across the x-axis, (b) across the y-axis, and (c) across the origin
1. (1,4)
2. (2, -3)
3. Define an even function and give an example.
4. Define an odd function and give an example.
5. Find equations for the vertical and horizontal lines through the point (1, 3).
In exercises 6 through 9, write an equation for the given line:
6.. P(2,3), m = 2
7. P(2,3), m=0
8. P(1,0), no slope
9. P(-1,2), m=-1/2
10. Given : P(6, 0) L: 2x – y = -2
A. Find an equation for the line through P parallel to L.
B. Find an equation of the line through P perpendicular to L.
Sketch the graphs below from memory. State the domain and range.
11. y  ( x  1) 2  3
12. y  x 3
1
17. y 
x2
18. y  x  1 19. y  (.5)
14. y  e
13. y  x
x
x
15. y = ln x
 x  2

20. y    x 2
 x2

for
21. Write a piecewise (compound) function for the graph to the right.
1
; g ( x)  x 2  4
x
A. Find the domain and range of f and g.
B. Find the equations for f + g, f--1, f/g, f  g ,and g  f .
C. Find the domain and range for f  g ,and g  f .
22. Given : f ( x) 
23. Write an equation for the circle with center (2, 0) and radius 5.
24. Identify the center and radius of the circle x2 + y2 – 2x + 4y – 6 = 0.
25. Write and equation for the parabola with focus (0, 2) and directrix y = -2.
26. Find the focus and directrix for the parabola y = x2 – 4x + 4.
16. y 
1
x
 2  x  1
1  x  1
1 x  2
27. Find the vertices, foci, eccentricity, and sketch the ellipse.
x2 y2

1
36 16
28. Classify the conic given : 7x2 – 12y2 – 14x + 24y – 28 = 0.
29. Put in standard form by completing the square and sketch. x 2  4 y 2  6 x  8 y  9  0 .
30. Solve the system :
8 x  y  11
x  y  97
Solve and Check. Show all work.
31. x  1  x  6  1
32. 8 2 x 3  4  2 x 1
x  1 5x
1


3x  6 6 x  2
33.
Simplify
x 2  2ax x 2  3ax  2a 2 x  2a
34.


2a  x
xa
a2  x2
1

35. x
1

x
1
x 1
1
x 1
36.
3 2
2 3 5
Evaluate
37.
 16  169
38. log327
 1 
39. 

 625 

3
4
40. ln(e2)
41. Which of the following has a vertical asymptote and why?
a) y  2x 2
b) y 
2
x3
c) y  x  1
d) y 
8x 3  1
2 x 2  5x  3
42. Write an equation for the polynomial graphed at right.
43. Solve each of the following by factoring.
a) x 2  6 x  8
b) 2m 2  6m
c) 3 x 2  2   x