Arithmetic Sequences
Linear Functions
Domain and Range
Characteristics
Parent Functions
100
What is the common difference in the sequence
{10, 13, 16, 19, 22,...}
The common difference is 3.
100
A bicycle rental shop charges a $10 starting fee and $7 per hour. Let h represent the number of hours represented, and let R(h) represent the total rental cost. Write function correctly models this situation.
R(h)=7h+10
100
Determine if the following statement is true or false. If it is false, fix the statement.
"When writing the domain and range, we use square brackets [ and ] when a value is NOT included in the function."
False.
"When writing the domain and range, we use square parentheses ( and ) when a value is NOT included in the function."
OR
"When writing the domain and range, we use square brackets [ and ] when a value IS included in the function."
100
Determine the end behavior for the function f(x)=x.
As x\to-\infty , f(x)\to _____
As x\to\infty , f(x)\to _____
As x\to-\infty , f(x)\to\infty
As x\to\infty , f(x)\to-\infty
100
Which of the following parent functions is the graph for the function f(x)=x^2 ?
B
200
A student saves $15 during the first week and increases the amount saved by $5 each week. If a_1=15 , write explicit function represents the total amount saved in the nth week.
a_n=15+5(n-1)
200
Determine f(-2) based on the graph below.
f(-2)=1
200
What is the domain and range of the function given by f(x)=x .
D: (-\infty, \infty)
R: (-\infty, \infty)
200
A water tank contains 150 gallons of water and drains at a constant rate of 10 gallons per minute. The amount of water remaining is modeled by w(t)=150-10t. What does the x-intercept (15, 0) represent in this situation?
At 15 minutes, there is no water remaining in the tank.
200
Which of the following parent functions has a domain of all real numbers? Select all that apply.
A, B, C, D, and F.
300
Based on the graph below, determine the common difference and write the explicit rule.
The graph is increasing by 4 each time.
a_n=2+4(n-1)
300
Determine the value of x when f(x)=2 using the table below.
x=-1
300
A kayak rental company charges a $15 starting fee plus $12 per hour. A customer may rent a kayak for up to 6 hours. The total cost is modeled by C(h) =12h+15 for 0 ≤ h ≤ 6 . Write the domain and range in interval notation.
D: [0,6]
R: [15,87]
300
A new business models its monthly profit, in thousands of dollars, by the function p(x)=3x-12 , where x represents the number of months since opening. Which statement correctly describes when the business has a positive profit?
A. Beginning at Month 4 and continuing after Month 4.
B. After Month 4, but not at Month 4.
C. Before Month 4.
D. From Month 0 through Month 4
B. After Month 4, but not at Month 4
300
Determine if the following statement is true or false. If it is false, correct the statement.
"The square root parent function f(x)=\sqrtx is nonlinear, begins at the origin, and has no graph for negative x-values in the real number system."
True.
400
An arithmetic sequence is defined explicitly by a_n=7+4(n-1) . Write the recursive equation that represents the same sequence.
a_n=a_(n-1)+4
a_1=7
400
A high school is selling tickets to a basketball game. The graph shows the total amount of money collected, M(t), based on the number of tickets sold, t. Each ticket costs $8. Write a statement correctly interprets M(30) = 240 in the context.
The school makes $240 for selling 30 tickets.
400
A discrete, linear function is best represented by f(x)=4x-10 and has a domain of {-2, 0, 2}. Determine the range.
R: {-18, -10, -2}
400
A rideshare driver starts the day with $20 in tips and earns tips at a constant rate throughout the next 5 hours. The graph shows the driver's total tips. State the domain and range in set builder notation. You must have both correct in order to receive points.
D: {x|0<=x<=5}
R: {y|20<=x<=70}
400
Which of the following parent functions does not include 0 as an x-value?
A
500
Consider the arithmetic sequence: {8, 13, 18, 23, ...}. What is the 45th term of this sequence?
The 45th term in the sequence is 228.
500
A bowling alley charges $6 shoe rental fee plus $4 for each game played. The total cost is represented by C(g)=4g+6 where g is the number of games played. What does C(5) represent in context, and what is its value?
The cost to play 5 games is $26.
500
A linear function is represented by a line segment with closed endpoints at (−3, 8) and (5, 24). What is the domain and range in interval notation?
D: [-3,5]
R: [8,24]
500
The table shows the height of a candle, f(x), as it burns each hour, x. Calculate the slope and interpret what it means in context.
The slope of the function is -3. That means the candle height is decreasing 3 centimeters every hour.
500
Which of the parent functions below has a range of (-\infty,infty) ? Select ALL that apply.
C and F.