Solve Equations
System of Equations
Functions
Arithmetic Sequences
Interpret Functions
Function Characteristics
100
Solve the equation 14 = ax + 6 for x.
x = 8/a
100
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)
D. (3, 1)
100
Why is this mapping not a function?
The input value "1" is mapped to two output values, "1" and "5."
In a function every input has exactly one output.
100
B. an = an – 1 + 2
100
A manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 5,000 + 1.3x.
What is the reasonable domain of the function?
x > 0
Since x represents a number of manufactured items, it cannot be negative, nor can a fraction of an item be manufactured. Therefore, the domain can only include values that are whole numbers.
100
Which function has a greater y-intercept?
A. f(x) = x + 5
B. g(x) = 2x – 5
C. h(x) = –2x.
A. f(x) = x + 5
200
This equation can be used to find h, the number of hours it will take Flo and Bryan to mow their lawn.
h/3 + h/6 =1
How many hours will it take them to mow their lawn?
A. 6 hours
B. 3 hours
C. 2 hours
D. 1 hour
C. 2 hours
200
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)
C. (2, 3)
200
Which set of Ordered Pairs represent a function?
Set I: {(1, 1), (1, 2), (2, 4), (3, 3)}
Set II: {(1, 1), (1, 5), (2, 3), (3, 3)}
Set III: {(1, 1), (2, 3), (3, 5)}
Set III
200
B. an=an-1 + 3
200
A manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 5,000 + 1.3x.
What is the cost of 2,000 items?
$7,600
200
Which function has a greater average rate of change?
A. f(x) = x + 5
B. g(x) = 2x – 5
C. h(x) = –2x.
B. g(x) = 2x – 5
300
2. A ferry boat carries passengers back and forth between two communities on the Peachville River.
• It takes 30 minutes longer for the ferry to make the trip upstream than downstream.
• The ferry’s average speed in still water is 15 miles per hour.
• The river’s current is usually 5 miles per hour.
This equation can be used to determine how many miles the two communities are apart.
m/(15 – 5) = m/(15+5) +0.5
What is m, the distance between the two communities?
A. 0.5 mile
B. 5 miles
C. 10 miles
D. 15 miles
C. 10 miles
300
Look at the tables of values for two linear functions, f(x) and g(x).
What is the solution to f(x) = g(x)?
x = 3
300
Given f(x) = 2x – 1, find f(7).
f(7) = 13
300
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
D. f(x) = 3x + 5
300
A manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 5,000 + 1.3x.
If costs must be kept below $10,000 this month, what is the greatest number of items she can manufacture?
3846 items
--------------solution
C(x) < 10,000
5,000 + 1.3x < 10,000
1.3x < 5,000
x < 3,846.2, or 3,846 items
300
What is the y- intercept?
A. (0, 6)
B. (0, 3)
C. (-3, 0)
D. (0, -3)
D. (0, -3)
400
For what values of x is the inequality
2/3 + x/3 >1
true?
A. x < 1
B. x > 1
C. x < 5
D. x > 5
B. x > 1
400
Which ordered pair is a solution of
3y + 2 = 2x – 5 ?
A. (–5, 2)
B. (0, –5)
C. (5, 1)
D. (7, 5)
C. (5, 1)
400
If g(6) = 3 – 5(6), what is g(x)?
g(x) = 3 – 5x
400
Which explicit formula describes the pattern in this table?
A. d = 3.14 × C
B. 3.14 × C = d
C. 31.4 × 10 = C
D. C = 3.14 × d
D. C = 3.14 × d
400
Does the graph of the function have an x-intercept, and if so what does that represent?
The x-intercept is 16. This means that the truck is fully paid off after 16 months of payments.
400
Where is the line decreasing?
A. n/a
B. (-infinity, infinity) or All Real values
C. x < 6
D. x > 6
A. n/a
500
Look at the steps used when solving 3(x – 2) = 3 for x.
3(x – 2) = 3 Write the original equation.
3x – 6 = 3 Use the Distributive Property.
3x – 6 + 6 = 3 + 6 Step 1
3x = 9 Step 2
3x/3 = 9/3 Step 3
x = 3 Step 4
Which step is the result of combining like terms? A. Step 1
B. Step 2
C. Step 3
D. Step 4
B. Step 2
500
A manager is comparing the cost of buying baseball caps from two different companies.
• Company X charges a $50 fee plus $7 per baseball cap.
• Company Y charges a $30 fee plus $9 per baseball cap.
For what number of baseball caps will the cost be the same at both companies?
A. 10
B. 20
C. 40
D. 100
A. 10
500
If f(–2) = –4(–2), what is f(b)?
f(b) = –4b
500
5. 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
C. f(x) = 4x – 20
500
Does the function increase or decrease?
The function decreases.
500
Where is the function positive?
A. x < 6
B. x = 6
C. x > 6
C. x > 6
600
Solve.
(-x)/4 < (x+2)/3
x > (-8)/7
600
A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased?
A. 3
B. 6
C. 9
D. 18
B. 6
600
Which is the equation for the graph?
f(x) = 2x -1
600
Each week, Tim wants to increase the number of sit-ups he does daily by 2 sit-ups. The first week, he does 15 sit-ups each day.
Write an explicit function in the form f(n) = mn + b to represent the number of sit-ups, f(n), Tim does daily in week n.
f(n) = 2n + 13
----->
roc/d/m: 2
y-int: 13
600
What is the y-intercept of the graph of the function in terms of the amount left to pay on the truck?
The y-intercept is 28,000, which means at zero months, the amount left to pay on the truck had not yet decreased. The cost of the truck.
600
C
700
Which graph represents a system of linear equations that has multiple common coordinate pairs?
B.
700
Which inequality matches the graph?
A. -x + 2y > 4
B. y < -1/2x + 4
C. x + 2y < 4
D. -1/2x + y < 4
C. x + 2y < 4
700
Each week, Tim wants to increase the number of sit-ups he does daily by 2 sit-ups. The first week, he does 15 sit-ups each day.
A recursive function in the form f(n + 1) = f(n) + d, where f(1) = a, can be written for the sit-up problem. What recursive function represents the number of sit-ups, f(n), Tim does daily in week n?
f(n + 1) = f(n) + 2,
where f(1) = 15 and d =2.
700
1. A wild horse runs at a rate of 8 miles an hour for 6 hours. Let y be the distance, in miles, the horse travels for a given amount of time, x, in hours. This situation can be modeled by a function.
Which of these describes the domain of the function?
A. 0 ≤ x ≤ 6
B. 0 ≤ y ≤ 6
C. 0 ≤ x ≤ 48
D. 0 ≤ y ≤ 48
A. 0 ≤ x ≤ 6
700
B