coordinate algebra practice eoct answers unit 3 · #1 two lines are graphed on this coordinate unit...

Coordinate Algebra

Practice

EOCT Answers

Unit 3

#1 Unit 3 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)

#2 Unit 3 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)

#3 Unit 3 The first term in this sequence is –1.

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 Unit 3 Which function represents the sequence?

A. an = an-1 + 1

Note: a1 = –1

a2 = a2-1 + 1

= a1 + 1

= –1 + 1

= 0

Equation A

is not answer,

since a2 1

First, test

Equation A

#3 Unit 3 Which function represents the sequence?

B. an = an-1 + 2

Note: a1 = –1

a2 = a2-1 + 2 = a1 + 2 = –1 + 2 = 1

Next, test Equation B

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

Answer: B

#4 Unit 3 Which function is modeled in this table?

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.


A. f(x) = x + 7

B. f(x) = x + 9

C. f(x) = 2x + 5

D. f(x) = 3x + 5

First, test Equation A A. f(x) = x + 7

f(1) = 1 + 7 = 8

f(2) = 2 + 7 = 9

?

YES

YES

?

NO

NO


A. f(x) = x + 7

B. f(x) = x + 9

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

NO

Next, test Equation C

C. f(x) = 2x + 5

f(1) = 2(1) + 5

= 2 + 5 = 7 NO


A. f(x) = x + 7

B. f(x) = x + 9

C. f(x) = 2x + 5

D. f(x) = 3x + 5

? YES

Next, test Equation D

C. f(x) = 3x + 5

f(1) = 3(1)+5 = 3+5 = 8

f(2) = 3(2)+5 = 6+5 = 11

f(3) = 3(3)+5

= 9+5 = 14

f(4) = 3(4)+5

= 12+5 = 17

YES

?

YES

YES

?

YES

YES

?

YES

YES

#5 Unit 3 Which explicit formula describes the

pattern in this table?

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.

A. d = 3.14 × C

B. 3.14 × C = d

C. 31.4 × 10 = C

D. C = 3.14 × d



A. d = 3.14 × C

B. 3.14 × C = d

C. 31.4 × 10 = C

D. C = 3.14 × d

Test answer A

A. d = 3.14 × C

2 = 3.14 × 6.28

2 19.72

Test answer B

NO 3.14 × 6.28 = 2

19.72 2

B. 3.14 × C = d

NO



A. d = 3.14 × C

B. 3.14 × C = d

C. 31.4 × 10 = C

D. C = 3.14 × d

Test answer C

C. 31.4 × 10 = C

31.4 × 10 = 6.28

314 6.28

Test answer D

NO 6.28 = 3.14 × 2

6.28 6.28

D. C = 3.14 × d

YES

#6 Unit 3 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

#7 Unit 3 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

#8 Unit 3 A population of squirrels doubles every year. Initially

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 Unit 3 The function graphed on this coordinate grid

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

#10

Unit 3 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?

C(x) = 5x + 3

Formula to model cost of renting canoe

x: # of hours rented

C: Total rental cost

The graph should be a line with

a slope of 5 and y-intercept of 3.

#10




A. Answer A is incorrect.

First, the graph is not linear.

The graph has a y-intercept = 0,

but the Cost Formula has a

y-intercept = 3.

C(x) = 5x + 3 Cost Formula:

#10




y = 5 D. The graph is a Horizontal Line.


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.)

#10




B.


Answer B is incorrect. The

graph has a y-intercept = 5,

but the Cost Formula has a

y-intercept = 3.

#10




C.


Answer C is correct. The

graph and Cost Formula

have a y-intercept = 3.

#11 Unit 3 Juan and Patti decided to see who could read

the most books in a month. They began to keep

track after Patti had already read 5 books that

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 Unit 3 Juan and Patti decided to see who could read the most

books in a month. They began to keep track after Patti

had already read 5 books that 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 2: Calculate the rate of

books to days for Patti in 8 days.

8 days

8

10

Step 3: If Juan read at the same

rate as Patti, then by day 12 he

would have also read 10 books.

Thus, the number of books Patti

read in 8 days was 10 books.

#12 Unit 3 Which function represents this sequence?

Use geometric sequence formula

an = a1 rn–1

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)

First Term: a1 = 6

3 3 3 3

Common Ratio: r = 3

an = 6(3n–1)

#13 Unit 3 The first term in this sequence is 3.

Which function represents the sequence?

Use arithmetic sequence formula

an = a1 + d(n – 1)

First Term: a1 = 3

+7 +7 +7 +7

Common Difference: d = 7

an = 3 + 7(n – 1)

A. f(n) = n + 3

B. f(n) = 7n – 4

C. f(n) = 3n + 7

D. f(n) = n + 7 = 3 + 7n – 7 = 7n – 4

#14 Unit 3 The points (0, 1), (1, 5), (2, 25), (3, 125) are

on the graph of a function. Which equation

represents that function?

A. f(x) = 2x

B. f(x) = 3x

C. f(x) = 4x

D. f(x) = 5x

Strategy: Test one or more of the

points in each equation to

see if both coordinates work.

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 Unit 3 A function g is an odd function.

If g(–3) = 4, which other point lies

on the graph of g?

Note: g(–3)=4 rewritten as

a point is (–3,4) A. (3, –4)

B. (–3, –4)

C. (4, –3)

D. (–4, 3)

Odd Function Rule

(x,y) (–x, –y)

Answer

(–3,4) (3, –4)

#16 Unit 3 Which statement is true about

the function f (x) = 7?

A. The function is odd because –f(x) = f(–x).

B. The function is even because –f(x) = f(–x).

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.

Odd function rule

#17 Unit 3 Which scatter plot BEST represents a

model of linear growth?

A.

C.

B.

D.

Linear

Growth

Linear

Exponential

Growth

No

Correlation

Negative

Correlation

#18 Unit 3 Which scatter plot BEST represents a

model of exponential growth?

A. B.

C. D.

Linear

Growth

Exponential

Growth

Linear

Decay

Weak

Linear

Growth Negative

Correlation

#19 Unit 3 Which table represents an

exponential function?

C.

A.

B.

D.

#20 Unit 3 If the parent function is f(x) = mx + b, what

is the value of the parameter m for the line

passing through the points (–2, 7) and (4, 3)?

1 2 2 1

1 2 2 1

OR y y y y

m mx x x x

m represents the slope of a line

Formula for the slope m of a line passing

through the points (x1,y1) and (x2,y2)

Slope m of line passing through

points (–2,7) and (4,3)

7 3 4 2=

2 4 6 3m

2

3

3

2

A. –9

B.

C. –2

D.

coordinate algebra practice eoct answers unit 3 · #1 two lines are graphed on this coordinate unit...

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