```Coordinate Algebra
Practice
Unit 3
#1 Two lines are graphed on this coordinate
plane. Which point appears to be a
solution of the equations of both lines?
A. (0, –2)
B. (0, 4)
C. (2, 0)
D. (3, 1)

Unit 3
#2
Based on the tables, at what point do the
lines y = –x + 5 and y = 2x – 1 intersect?
A. (1, 1)
B. (3, 5)
C. (2, 3)
D. (3, 2)
Unit 3
#3
The first term in this sequence is –1.
Unit 3
Which function represents the sequence?
A. an = an-1 + 1
B. an = an-1 + 2
C. an = 2an-1 – 1
D. an = 2an-1 – 3
Strategy:
Use table to substitute n into each
equation. Then, simplify and
determine whether the result is the
value of an in the table.
#3
Which function represents the sequence?
Note: a1 = –1
A. an = an-1 + 1
a2 = a2-1 + 1
= a1 + 1
= –1 + 1
=
0
Unit 3
First, test
Equation A
Equation A
since a2  1
#3
Which function represents the sequence?
Note: a1 = –1
A. an = an-1 + 1
a2 = a2-1 + 1
= a1 + 1
= –1 + 1
=
0
Unit 3
First, test
Equation A
Equation A
since a2  1
#3
Which function represents the sequence? Unit 3
Note: a1 = –1
Next, test Equation B
B. an = an-1 + 2
a2 = a2-1 + 2 = a1 + 2 = –1 + 2 = 1
a3 = a3-1 + 2 = a2 + 2 = 1 + 2 = 3
a4 = a4-1 + 2 = a3 + 2 = 3 + 2 = 5
a5 = a5-1 + 2 = a4 + 2 = 5 + 2 = 7
YES
YES
YES
YES
#4
Which function is modeled in this table?
Unit 3
A. f(x) = x + 7
B. f(x) = x + 9
C. f(x) = 2x + 5
D. f(x) = 3x + 5
Strategy:
Use table to substitute x into each equation.
Then, simplify and determine whether the
result is the value of f(x) in the table.
#4
Which function is modeled in this table?
Unit 3
A. f(x) = x + 7
? YES
? NO
B. f(x) = x + 9
C. f(x) = 2x + 5
D. f(x) = 3x + 5
A. f(x) = x + 7
f(1) = 1 + 7 = 8
f(2) = 2 + 7 = 9
First, test Equation A
YES
NO
#4
Which function is modeled in this table?
Unit 3
A. f(x) = x + 7
B. f(x) = x + 9
? NO
C. f(x) = 2x + 5
D. f(x) = 3x + 5
Next, test Equation B
B. f(x) = x + 9
f(1) = 1 + 9 = 10
NO
Next, test Equation C
C. f(x) = 2x + 5
f(1) = 2(1) + 5
= 2 + 5=7
NO
#4
Which function is modeled in this table?
Unit 3
A. f(x) = x + 7
B. f(x) = x + 9
C. f(x) = 2x + 5
D. f(x) = 3x + 5
Next, test Equation D
C. f(x) = 3x + 5
f(1) = 3(1)+5 = 3+5 = 8 YES
f(2) = 3(2)+5 = 6+5 = 11 YES
? YES
? YES
? YES
? YES
f(3) = 3(3)+5 YES
= 9+5 = 14
f(4) = 3(4)+5 YES
= 12+5 = 17
#5
Which explicit formula describes the
pattern in this table?
Unit 3
A. d = 3.14 &times; C
B. 3.14 &times; C = d
C. 31.4 &times; 10 = C
D. C = 3.14 &times; d
Strategy:
Use values in table to substitute d and C into
each equation. Then, simplify and determine
whether both sides of the equation are equal.
#5
Which explicit formula describes the
pattern in this table?
Unit 3
A. d = 3.14 &times; C
B. 3.14 &times; C = d
C. 31.4 &times; 10 = C
D. C = 3.14 &times; d
A. d = 3.14 &times; C
2 = 3.14 &times; 6.28
2  19.72
NO
B. 3.14 &times; C = d
3.14 &times; 6.28 = 2
19.72  2 NO
#5
Which explicit formula describes the
pattern in this table?
Unit 3
A. d = 3.14 &times; C
B. 3.14 &times; C = d
C. 31.4 &times; 10 = C
D. C = 3.14 &times; d
C. 31.4 &times; 10 = C
31.4 &times; 10 = 6.28
314  6.28 NO
D. C = 3.14 &times; d
6.28 = 3.14 &times; 2
6.28  6.28 YES
#6
If f(12) = 4(12) – 20,
which function gives f(x)?
A. f(x) = 4x
B. f(x) = 12x
C. f(x) = 4x – 20
D. f(x) = 12x – 20
Unit 3
#7 A farmer owns a horse that can continuously run an
average of 8 miles an hour for up to 6 hours. Let y be
the distance the horse can travel for a given x amount
of time in hours. The horse’s progress can be modeled
by a function. Which of the following describes the
domain of the function?
A. 0 ≤ x ≤ 6
B. 0 ≤ y ≤ 6
C. 0 ≤ x ≤ 48
D. 0 ≤ y ≤ 48
Unit 3
#8 A population of squirrels doubles every year. Initially Unit 3
there were 5 squirrels. A biologist studying the
squirrels created a function to model their population
growth, P(t) = 5(2t) where t is time. The graph of the
function is shown. What is the range of the function?
A. any real number
B. any whole number
greater than 0
C. any whole number
greater than 5
D. any whole number
greater than or
equal to 5
#9
The function graphed on this coordinate grid Unit 3
shows f(x), the height of a dropped ball in
feet after its xth bounce. On which bounce
was the height of the ball 10 feet?
A. bounce 1
B. bounce 2
C. bounce 3
D. bounce 4

Unit 3
#10
To rent a canoe, the cost is \$3 for the oars and life
preserver, plus \$5 an hour for the canoe. Which
graph models the cost of renting a canoe?
Formula to model cost of renting canoe
x: # of hours rented
C: Total rental cost
C(x) = 5x + 3
The graph should be a line with
a slope of 5 and y-intercept of 3.
Unit 3
#10
To rent a canoe, the cost is \$3 for the oars and life
preserver, plus \$5 an hour for the canoe. Which
graph models the cost of renting a canoe?
Cost Formula: C(x) = 5x + 3
A.

First, the graph is not linear.
The graph has a y-intercept = 0,
but the Cost Formula has a
y-intercept = 3.
Unit 3
#10
To rent a canoe, the cost is \$3 for the oars and life
preserver, plus \$5 an hour for the canoe. Which
graph models the cost of renting a canoe?
Cost Formula: C(x) = 5x + 3
D.
The graph is a Horizontal Line.
y=5
Answer D is incorrect. The equation
y = 5 concludes that the total rental
cost will be \$5, regardless of the
number of hours rental. (i.e. The
canoe rental cost would be \$5, if
rented for 1 hour or 20 hours.)
To rent a canoe, the cost is \$3 for the oars and life
preserver, plus \$5 an hour for the canoe. Which
graph models the cost of renting a canoe?
Unit 3
#10
Cost Formula: C(x) = 5x + 3
B.

graph has a y-intercept = 5,
but the Cost Formula has a
y-intercept = 3.
Unit 3
#10
To rent a canoe, the cost is \$3 for the oars and life
preserver, plus \$5 an hour for the canoe. Which
graph models the cost of renting a canoe?
Cost Formula: C(x) = 5x + 3
C.
graph and Cost Formula
have a y-intercept = 3.

#11
Juan and Patti decided to see who could read Unit 3
the most books in a month. They began to keep
month. This graph shows the number of books
Patti read for the next 10 days.
If Juan has read no books
before the fourth day of the
month and he reads at the same
rate as Patti, how many books
will he have read by day 12?
Step 1: Determine the time that
passes for Juan to read from
day 4 to day 12 (12–4 = 8 days)
8 days
#11
Juan and Patti decided to see who could read the most Unit 3
books in a month. They began to keep track after Patti
the number of books Patti read for the next 10 days.
If Juan has read no books before the
fourth day of the month and he reads
at the same rate as Patti, how many
books will he have read by day 12?
10
8
8 days
Step 2: Calculate the rate of
books to days for Patti in 8 days.
Thus, the number of books Patti
read in 8 days was 10 books.
Step 3: If Juan read at the same
rate as Patti, then by day 12 he
would have also read 10 books.
#12
Which function represents this sequence?
3
A. f(n) =
3n-1
B. f(n) = 6 n-1
C. f(n) = 3(6 n-1)
D. f(n) = 6(3 n-1)
3
3
Unit 3
3
Use geometric sequence formula
an = a1  rn–1
First Term: a1 = 6
Common Ratio: r = 3
an = 6(3n–1)
#13
The first term in this sequence is 3.
Which function represents the sequence?
+7
Unit 3
+7 +7
+7
Use arithmetic sequence formula
A. f(n) = n + 3
an = a1 + d(n – 1)
B. f(n) = 7n – 4
First Term: a1 = 3
Common Difference: d = 7
C. f(n) = 3n + 7
D. f(n) = n + 7
an = 3 + 7(n – 1)
= 3 + 7n – 7 = 7n – 4
Unit 3
#14
The points (0, 1), (1, 5), (2, 25), (3, 125) are
on the graph of a function. Which equation
represents that function?
Strategy: Test one or more of the
A. f(x) = 2x
points in each equation to
see if both coordinates work.
B. f(x) = 3x
C. f(x) =
4x
D. f(x) = 5x
Try the point (1,5)
Substitute 1 for x. If the answer is 5,
then the equation works.
A. f(1) = 21 = 2
B. f(1) = 31 = 3
C. f(1) = 41 = 4
D. f(1) = 51 = 5
#15
A function g is an odd function.
If g(–3) = 4, which other point lies
on the graph of g?
A. (3, –4)
B. (–3, –4)
C. (4, –3)
D. (–4, 3)
Note: g(–3)=4 rewritten as
a point is (–3,4)
Odd Function Rule
(x,y)  (–x, –y)
(–3,4)  (3, –4)
Unit 3
#16
the function f (x) = 7?
Unit 3
A. The function is odd because –f(x) = f(–x).
B. The function is even because –f(x) = f(–x).
Odd function rule
C. The function is odd because f(x) = f(–x).
D. The function is even because f(x) = f(–x).
Note: f (x) = 7 is the equation of a horizontal line.
It can be rewritten as y = 7.
Every horizontal line is an even function.
#17
A.
C.
Which scatter plot BEST represents a
model of linear growth?
Exponential
Growth
Linear
Negative
Correlation
B.
Linear
Growth
D.
No
Correlation
Unit 3
#18
Which scatter plot BEST represents a
model of exponential growth?
A.
C.
Unit 3
B.
Exponential
Growth
Linear
Growth
D.
Linear
Decay
Negative
Correlation
Weak
Linear
Growth
Which table represents an
exponential function?
#19
A.
B.
C.
D.
Unit 3
If the parent function is f(x) = mx + b, what Unit 3
is the value of the parameter m for the line
passing through the points (–2, 7) and (4, 3)?
#20
A. –9
B. 
3
2
C. –2
D. 
2
3
m represents the slope of a line
Formula for the slope m of a line passing
through the points (x1,y1) and (x2,y2)
m 
y1  y 2
x1  x 2
OR
m 
y 2  y1
x 2  x1
Slope m of line passing through
points (–2,7) and (4,3)
m 
73
2  4
= 
4
6
 
2
3
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