Name: ________________________
Calculus, Study Guide, Chapter P
1. Find the points of intersection of the graphs of the equations:
x  y 2  23
y  x3
 7

radians  .
2. Find the exact value of cos  
 4

3. y = sin 3
Sketch the graph of the tangent curve in the interval from 0 to 2 .
4. y = tan 2
What values for  (0   < 2satisfy the equation?
5. 5tan  6  tan
3
6. tan 2    sec 
2
7. 2 sin  cos   cos   0
Find the height of the triangle.
8.
9. Find all intercepts:
y  x  5
4  x2
10. Find all intercepts:
y 2  x 3  25x
9
11. Find an equation of the line that passes through the point (11,  9) and has the slope m  .
2
 8
 3
70 
21 
12. Find an equation of the line that passes through the points   ,   and  ,   .
 2
11 
4 
 11
13. Write an equation of the line that passes through the given point and is perpendicular to the given line.
Point
Line
 1, 7 


x6
 5 5 
14. Write an equation of the line that passes through the point  ,  and is parallel to the line 7x  3y  0.
 4 8 
15. Let f x  14x  8. Then simplify the expression
f(x)  f(9)
.
x9
16. Find the domain and range of the function f(x)  x 2  6.
17. Find the domain and range of the function h(x) 
11
.
x6
ID: A
Calculus, Study Guide, Chapter P
Answer Section
1.  2, 5  ,  7,  4 
2.
2
2
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
 5
,
4 4
2 4
,
3 3
 7 3 11
,
,
,
2 6
2
6
3.4
x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercept: (0, 10)
x-intercepts: (0,0), (5,0), (-5,0); y-intercept: (0, 0)
9
81
y x+
2
2
1
y  x6
2
ID: A
y  1
56x  24y  55  0
14
domain: (, )
range: [6, )
17. domain: (,  6)  (6, )
range: (, 0)  (0, )
13.
14.
15.
16.