Download Math 1330 Test 2 Review Example 1: Calculate the difference

Math 1330 Test 2 Review
Example 1: Calculate the difference quotient:
2

Example 2: Given f ( x)   0
x2

f ( x)   x 2  4 x 
1
8
x  1
x  1 , Find f (2)  f (2)
1  x
Example 3: Suppose f ( x)  2 x 2  x and g ( x)  x  1 . Find  f  g (x) .
Example 4: Suppose f ( x) 
x 1
and g ( x)  2 x  1 . Find  f  g (x) .
 3x  4
Math 1330 Test 2 Review
Example 5: Write the function f ( x)  3x 2  6 x  5 in the form f ( x)  a ( x  h) 2  k . Identify the vertex and
maximum/minimum value.
Example 6: Be able to functions from their graphs:
a.
b.
y




x













Math 1330 Test 2 Review
Example 7: Suppose f ( x) 
2x 1
. Find f 1 ( x)
x3
Example 8: Find the linear function f with a y intercept of  6 and f 1 (1)  2
Example 9: Assume the domain of f and f 1 is  ,   and f (2)  1 . Solve for x: f 1 ( x  4)  2 .
Example 10: Find any hole(s), vertical asymptote(s), horizontal asymptote and does the function cross the
horizontal asymptote in the following function:
2x2  4x
f ( x)  2
x 4
Math 1330 Test 2 Review
Example 11: Simplify :
log 2 2
log 2 3 2 2
Example 12: Graph f ( x)  3 x  2   9 . Find the domain, range, x-intercept and y-intercept and asymptote.
Example 13: Graph f ( x)  log 2 ( x  2)  2 . Find the domain, range, x-intercept and y-intercept and asymptote.
Example 14: Solve for x: log 4 ( x  1)  4
Math 1330 Test 2 Review
Example 15: Solve for x: log 7 ( x)  log 7 ( x  2)  log 7 (8)
Example 16: Solve for x: log 2 ( x  5)  4  log 2 ( x  1)
Example 17: Let θ be an acute angle of a right triangle and that
trigonometric functions of θ.
. Find all the rest of the
Math 1330 Test 2 Review
Example 18: Let θ be an acute angle of a right triangle and that
. Find all the rest of the
trigonometric functions of θ.
Example 19: A sector of a circle has central angle θ = 2π/3 and area 16π/3 ft2.
a. Find the radius of the circle.
b. Find the length of the sector for the problem above.
Example 20: Find the area of the sector with a central angle of θ = 240° and a r = 6 cm
Math 1330 Test 2 Review
Example 21: A car has wheels with a 10 cm radius. If each wheel’s rate of turn is 3 revolutions per second
a. What is the angular speed?
b. How fast is the car moving in units of cm/sec, (linear speed)?
Example 22: Find three angles, two positive and one negative, which are coterminal with the given angle:
Example 23: Evaluate the following.
4 
sin

 3 
 5 
tan

 6 
2
cot  
 3 
 5 
cos 
 4 
 5 
sec 
 6 

csc 
3
Example 24: Simplify
14 
sin

 3 
a.
4
3
Math 1330 Test 2 Review
 16 
tan

 3 
b.
34 
 17 
4 cos
  cot 

 6 
 4 
c.
Example 25: Simplify:
Math 1330 Test 2 Review
Example 26: Simplify
a.
b.
Math 1330 Test 2 Review
Example 27: Fill in the unit circle