Deck 1: Precalculus Review

Question 1

Complete the statement: if and then which of the following must be true:

A) .
B) .
C) .
D) .
E)

Answer 1

.

Question 2

Find the greatest and smallest values of such that satisfies the inequalities and .

Answer 2

Question 3

Determine whether the following functions are even, odd or neither:

A)
B)
C)
D)

Answer 3

A) Even
B) Odd
C) Even
D) Neither

Question 4

State whether the following functions are even, odd, or neither:

A)
B)
C)
D)

Question 5

Find the minimum and maximum values of for satisfying and .

Question 6

Find domain and range of the function .

Question 7

State whether the following functions are even, odd or neither:

A)
B)
C)
D)

Question 8

Find the maximum value of for .

Question 9

Find the smallest and the largest values of that satisfy each of the following inequalities:

A)
B)

Question 10

What are the smallest and largest values of satisfying and ?

Question 11

Find the radius of the circle with center passing through .

Question 12

Find the greatest and smallest values of such that satisfies the inequalities and .

Question 13

Find an equation of the circle passing through and whose center is located at the midpoint of the line segment joining and .

Question 14

Find the greatest and the smallest values of such that satisfies the inequalities and .

Question 15

Find the interval over which the function is increasing.

Question 16

Find the minimum and maximum values of if .

Question 17

Suppose that is even and is odd. Determine whether the following functions are even, odd, or neither:

A)
B)
C)
D)

Question 18

Complete the statement:
If and then,

A)
B)
C)
D)
E)

Question 19

Suppose that . What are the minimum and maximum possible values of ?

Question 20

Find the interval over which the function is increasing.

Question 21

Find the point on the line closest to the point .

Question 22

Find the maximum value of for .

Question 23

What is the distance between the maximum point on the parabola and the minimum point on the parabola .

Question 24

A line is perpendicular to and passes through . Find the coordinate of the point on the line where .

Question 25

Let , . Find the value of such that the points and are farthest for .

Question 26

Find such that lies on the line of slope through the point

Question 27

Find the constants and of the line with -intercept at , and which is perpendicular to the line .

Question 28

Find the point on the line closest to the origin. What is the distance between the two points?

Question 29

What is the maximum possible value of for ?

Question 30

Find the point of intersection of the following lines:
The line of slope 2 passing through the midpoint of the segment joining the points and .
The line perpendicular to and passing through .

Question 31

Find the point of intersection of the following lines:
The line parallel to and passing through the midpoint of the segment connecting the points and .
The line perpendicular to and passing through .

Question 32

The line in the figure is parallel to the diagonal of the rectangle.
Find the -coordinate of .

Question 33

For which values of does the parabola have no real roots?

Question 34

Find the point on the line closest to the point . What is the distance between the two points?

Question 35

What is the maximum value of if

Question 36

Referring to the figure, find the equation of the line containing the altitude from Point to side of the triangle. What is the -coordinate of the point on this line with ?

Question 37

What is the maximum possible value of if ?

Question 38

Find the point on the line that is closest to the point . What is the distance between the two points?

Question 39

Find an equation of the line perpendicular to and passing through . What is the -coordinate of the point on this line with ?

Question 40

Complete the square and find the maximum value of .

Question 41

Let and . Find all values of such that the domain of is all .

Question 42

Find the points of intersection of the graphs of and for .

Question 43

The domain and range of are:

A) Domain: Range:
B) Domain: Range:
C) Domain: Range:
D) Domain: Range:
E) Domain: Range:

Question 44

Let and . Compute the composite functions and and determine their domains.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 45

Let and . Calculate the composite functions and and determine their domains.

A)
B)
C)
D)
E)

Question 46

Given and . Calculate the composite functions and and determine their domains.

A)
B)
C)
D)
E)

Question 47

Let and .
Find all values of such that the domain of is all of .

Question 48

Let and .
Find all values of so that the domain of is all .

Question 49

Let and . Calculate the composite function and determine its domain and range.

Question 50

Let . Find all values of such that the domain of is all .

Question 51

The domain and the range of the function are:

A) Domain Range:
B) Domain: Range:
C) Domain Range:
D) Domain Range:
E) Domain: Range:

Question 52

Find , , and if and is acute.

Question 53

Find , , and if and .

Question 54

The domain and range of the function are:

A) Domain: Range:
B) Domain: Range:
C) Domain: Range:
D) Domain: Range:
E) Domain: Range:

Question 55

Solve the following equation for if : .

Question 56

Let and Calculate the composite functions and and determine their domains.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 57

Solve the following equation for if : .

Question 58

Find the minimum value of the angle between the segment joining a point on the graph of with the origin, and the -axis for .

Question 59

The domain and range of are:

A) Domain: Range:
B) Domain: Range:
C) Domain: Range:
D) Domain: Range:
E) Domain: Range:

Question 60

Solve the following equation for if : .

Question 61

Find all vertical and horizontal asymptotes for the function .

Question 62

Find and if and .

Question 63

Find the points where the graphs of and intersect for .

Question 64

Find , , and if and is acute.

Question 65

Find the set of solutions to the inequality .

Question 66

Find the points of intersection of the two graphs and for .

Question 67

Solve the following equation for if : .

Question 68

Referring to the figure, find the value of .

Question 69

Find , , and if and is acute.

Question 70

Use the addition formula to compute exactly.

Question 71

Solve the following equation for if : .

Question 72

Find the points of intersection of the graphs of and for .

Question 73

Find if and

Question 74

Referring to the figure, compute the value of .