Understand Functions
Compare Functions
Interpret Equations
Construct Linear Functions
Vocabulary
100
Which relation represents a function?
A. B.
C. D.
C. There is one input for every output.
100
The relationship between one set of variables is modeled by y= -2x+8 .
A second functional relationship is represented by this graph.
Which statement about the two functions is true?
A. The rates of change for the two functions are equal.
B. The rate of change is positive for the first function and negative for the second function.
C. The rate of change in the first function is 4 times greater than the rate of change in the second function.
D. The rates of change for the two functions are negative inverses.
A. The graph has a rate of change of -2, the same as the equation.
100
Which of these can be the graph of the equation y=mx+b ?
A. B.
C. D.
A. Any equation in the form of y=mx+b is a linear equation. Linear equations are straight lines.
100
Gwen read the first 15 pages of a book in a bookstore and decided to buy it. Since she bought it, she has been reading 30 pages per day. For which of these functions does y represent the total number of pages Gwen has read if x represents the number of days since she bought the book?
A. x=15y+30
B. x=30y+15
C. y=15x+30
D. y=30x+15
D. She initially read 15. That is added to the 30x to represent 30 pages each day.
100
Function
A rule that assigns exactly one output to each input.
200
Which of the following relations between input numbers and output numbers is not a function?
A. B.
C. D.
B. The input 2 has two outputs.
200
Line L passes through the points (-3,2) and (5,-1) . Line M has the equation: y= 2/3x - 4.
Which statement is true?
A. Line L has a negative slope and line M has a positive slope.
B. Line L has a positive slope and line M has a negative slope.
C. Both lines have negative slopes.
D. Both lines have positive slopes.
A. Line L has a negative slope and line M has a positive slope.
The slope of L is -3/8 and the slope of M is 2/3.
200
The graph of a function contains the points (6, 7) and (10, 13). Which of these statements is correct based on this information?
A. If the graph also contains the point (1, 2), then the function could be linear.
B. If the graph also contains the point (4, 4), then the function must not be linear.
C. If the graph also contains the point (8, 10), then the function could be linear.
D. If the graph also contains the point (12, 16), then the function must not be linear.
C. set up a table and find constant rate of change.
200
Hector purchased a used car and the graph below shows the number of miles on the car since he bought it. Which of these is a correct statement based on the graph?
A. Hector is driving the car 2,000 miles per month.
B. Hector is driving the car 3,000 miles per month.
C. The car had 2,000 miles on it when Hector bought it.
D. The car had 3,000 miles on it when Hector bought it.
C. The graph starts at 2 = 2,000 miles.
200
Domain
The set of all possible input values.
300
Which table represents a function?
A. B.
C. D.
C. There are no duplicate x values.
300
Fabian plots the linear function f below.
Gina graphs function g, which is a straight line that passes through (0, 8) and (8, 7).
Which of these correctly describes the slopes of f and g?
A. f has a slope of –8 and g has a slope of - 1/8 .
B. Both f and g have a slope of -8
C. f has a slope of -1/8 and g has a slope of –8.
D. Both f and g have a slope of -1/8.
D. Both f and g have a slope of -1/8 . Any points on the same line will have the same slope.
300
Select the linear function.
A. y= x/8 - 4
B. y= 6/x - 2
C. y= x^2/4 - 6
D. y= 4x^3
A. x has a power of one = linear
-x cannot be denominator
-x cannot be raised to any power greater than 1
300
A hot air balloon was flying at an altitude of 300 meters when the pilot decided to land by descending at a rate of 2 meters per second. For which of these functions does y represent the altitude of the hot air balloon if x represents the number of seconds since the pilot started her landing?
A. y= -2x - 300
B. y= -2x + 300
C. y= 2x - 300
D. y= 2x + 300
B. Initial start is +300 and then descends represented by a negative.
300
The set of all possible output values.
Range
400
Which of the following is the graph of a function?
A. B.
C. D.
C. This passes the vertical line test.
400
Ellen and Oscar are running a race. Ellen runs the first mile in 8 minutes, and then each additional mile in 11 minutes. Oscar’s speed is represented in the function t=10m, where t is the number of minutes it takes him to run m miles. Which statement is true?
A. If the race is 3 miles long, Ellen and Oscar finish at the same time.
B. If the race is 4 miles long, Ellen finishes ahead of Oscar.
C. If the race is 2 miles long, Oscar finishes ahead of Ellen.
D. If the race is 1 mile long, Oscar finishes ahead of Ellen.
A. Ellen's equation: 8+11m --> 8+11(2)= 30
Oscar's equation: 10m--> 10(3)= 30
400
Which of these statements correctly describes the function y= 8/x + 5 ?
A. It is a linear function, and its graph is a straight line.
B. It is a linear function, but its graph is not a straight line.
C. It is not a linear function, but its graph is a straight line.
D. It is not a linear function, and its graph is not a straight line.
D. x can never be the denominator and be linear.
400
A tree was 8 feet tall when it was planted. After 5 years, it was 18 feet tall. What was the tree’s growth rate?
A. 1.6 feet per year
B. 2 feet per year
C. 3.6 feet per year
D. 8 feet per year
B. 2 feet per year
The tree grew 18 – 8 = 10 feet in 5 years, so its growth rate was 10 ÷ 5 = 2 feet per year.
400
What is the independent variable?
Input value or Output Value
Input Value
500
Which table of values can be represented by the function y=2x+5 ?
A.
A. has a slope of 2 and y intercept of 5
500
Consider these two functions. The graph represents the first function.
The table represents the second function.
What conclusion can be made about the two functions?
A. The second function increases faster than the first function.
B. The functions’ rates of increase are negative inverses of each other.
C. The functions have an equal rate of increase.
D. The first function increases faster than the second function.
C. The functions have an equal rate of increase.
The slope of the line represented by each function is 2/3
500
Which equation describes a function that is NOT linear?
A. y= -8x
B. y= 4x-5
C. y= x/3
D. y=x^2 + 7
D.
This function cannot be written in the form y = mx + b because the x has an exponent of 2. This means it is not linear.
500
This table below shows the relationship between cars washed and money earned at a fundraising event.
According to the table, the fundraising event earned $_____ after 7 cars were washed.
The event earned $____per car.
$42 after 7 cars
$6 per car.
500
What is a linear function?
A function whose graph has a straight line