Download Quiz 1.
Checkpoint Quiz 1.1
Name:
1. Let P (2,−3) and Q(−5,−1)
(a) Plot P and Q.
(b) Determine the quadrants in which P and Q lie.
(c) Find the distance between P and Q.
(d) Find the midpoint of the line segment which connects P and Q.
(e) Find the point symmetric to P about the:
i. x-axis
ii. y-axis
iii. origin
2. Find all points on the y-axis which are 3 units from (−1, 5).
Checkpoint Quiz 1.
2
Name:
1. Sketch the following relations:
(a) {(−3, 2), (−1, 0), (0,−2), (1, 3)}
(b)
{(
n, 6
n
)
: n = ±1,±2,±3)
}
(c) {(x,−2) : x > 1}
(d) {(x, y) : x > 1, y ≤ 2}
(e) {(x, y) : x > 1, −1 < y ≤ 2}
2. Describe the following relations using the roster method.
(a)
x
y
−4 −3 −2 −1 1 2 3
4
−
1
1
2
3
4
The graph of relation A
(b)
x
y
−3 −2 −1 1 2 3
−3
−2
−1
1
2
3
The graph of relation B
Checkpoint Quiz 1.3
Name:
1. Consider the equation: (x − 1)2 − y2 = 25
• Find the x- and y-intercept(s) of the graph, if any exist.
• Create a table of sample points on the graph of the equation.
• Plot the sample points and create a rough sketch of the graph of the equation.
• Test for symmetry. If the equation appears to fail any of the symmetry tests, find a point on the
graph of the equation whose reflection fails to be on the graph.
Checkpoint Quiz 1.
4
Name:
1. Determine if the relation whose graph is below represents y as a function of x. If so, state the domain
and range using interval notation.
(a)
x
y
−4 −3 −2 −1
1
−1
1
2
3
4
(b)
x
y
−4 −3 −2 −1 1 2 3 4 5
−3
−2
−1
1
2
2. Does the equation y2 − y2x = 1 describe y as a function of x? Explain.
Checkpoint Quiz 1.5
Name:
1. Suppose f is a function that takes a real number x and performs the following steps in the order given:
(1) add 4
(2) take the square root
(3) subtract 5
(4) divide into 10
Find an expression for f (x) and state the domain of f using interval notation.
2. Let f (x) =
x2
x − 3
. Find and simplify the following:
(a) f (−1) (b) f (7x) (c) 7f (x) (d) f (x − 1)
3. Let f (x) =
{
3x − 1, x ≤ −4
−x2, x > −4
. Find f (−2), f (−4), and f (−5).
Checkpoint Quiz 1
.
6
Name:
1. Let f(x) = 2x + 6 and g(x) = x2 − 9.
Find the domain of the following functions and simplify their expressions.
(a) (g − f)(x) (b)
(
f
g
)
(x)
2. Let f(x) = −x2 + 2x− 3. Find and simplify the difference quotient, f(x + h)− f(x)
h
.
Checkpoint Quiz 1.8
Name:
1. The complete graph of y = f (x) is given below.
(0, 1)
(2, 3)
(4, 2)
(5, 0) x
y
1 2 3
4
2
3
4
5
y = f (x)
Let g(x) = 3 − f
(
1−x
2
)
. Sketch the graph of y = g(x). From your graph, determine the domain and
range of g. List the intervals over which g is increasing and the intervals over which g is decreasing.
List the local maximums and local minimums, if any.
2. Let f (x) = x2. Find a formula for a function g whose graph is obtained from the graph of y = f (x)
after the following sequence of transformations:
• Shift left 3 units.
• Reflection across the y-axis.
• Shift down 1 unit.
• Vertical scaling by a factor of 2.
• Reflection across the x-axis.