FUNCTION OR NOT
Real World Problems
Vocabulary
Random
Linear or Non linear
100
Which of the following graphs represents a relation that is NOT a function? Explain answer!
Graph Number 1. Does not pass the vertical line test. Line passes through two x coordinates.
100
The function p=17ℎ+100 represents Kevin’s pay per week, p, for h hours of work. Kevin makes $17 per hour and receives $100 to cover meal expenses. Kevin accepts a new job where his pay is represented by the graph shown.
How did Kevin’s pay change from his first job to his second job? (hint: find the slope of the graph)
His pay per hour increased by $3.
The answer shows the one change from the first job to the second job. Pay per hour in the first job was $17 and pay per hour in the second job is $20
100
What do we call the input of a function?
The domain (or x-value).
100
Which of the following ordered pairs satisfy the function y=-3x+4? Select ALL that apply.
A. (4,-8)
B. (2,-10)
C. (-1,7)
D. (-3,4)
(4,-8) and (-1,7)
100
Which equations are NOT linear? Select TWO that apply.
A.) y= 1/4 x + 1/16
B.) y= lxl + 1
C.) y= 2 + 1/x
D.) x= -6y
B and C
200
Determine whether or not each relation represents a function.
Relation A: Function
Relation B: Not a Function
Relation C: Function
Relation D: Function
200
Jacob ran his first 5K race.
- Jacob ran at a fast pace at the beginning and end of the race.
- He jogged slowly to conserve energy during the middle of the race.
Which sketch BEST illustrates Jacob’s 5K run?
This graph shows a fast and direct relationship in the beginning and end of the race when he was running fast and a slower but still direct relationship when he was jogging in the middle of the race.
200
What do we call the output of a function?
The range (or y-value).
200
What is the slope of this line?
change in y over change in x : 3/2
200
This graph represents a linear function. Write an equation to represent the graph.
y= 2/3 x -2
300
Write a statement that BEST describes why this set of ordered pairs is NOT a function?
{(1,5) , (2,6) , (3,6) , (4,1) , (4,20) ,(5,21) , (6,24)}
The x-value of 4 is paired with two different y-values.
300
A taxi cab company charges $8.00 per ride plus $0.75 for each mile driven. Which equation models the total cost (c), in dollars, of a taxi cab ride, where m is the number of miles driven?
A. c = 8m + 0.75
B. c = 8.75m + 0.75
C. c = 0.75m + 8
D. c = 0.75m + 8.75
C. c = 0.75m + 8
The initial value (base cost per ride) is 8, and the rate of change (cost per mile) is 0.75, which means the slope-intercept form equation that represents this scenario is c = 0.75m + 8.
300
What is a function?
A relation where each input has exactly one output.
300
The graph shows how the height of a balloon is changing over time.
What would the slope of this line tell us?
Rate at which the balloon is rising.
300
Which functions are nonlinear?
A.) y=-5
B.) y= x/3 +1
C.)
D.)
D. No constant rate of change
400
Which of the following relations between input numbers and output numbers is NOT a function?
A. B.
C. D.
Option C. The number 2 on the input has two outputs.
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?
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 test is used to determine if a graph represents a function?
The vertical line test.
400
Which equation has a greater rate of change than the linear function represented by points.
(-5, -18) , (-3, -8), (1,12), (3, 22)
A.) y= 5x - 3 B.) y= -4x - 18 C)y= 6x + 13
C) has a rate of change of 6 which is more than 5 from the data set.
400
Harriet believes that the function y=11x is linear, while Paul believes that it is not linear. Who is right, and why?
Harriet is right because any equation where the polynomial has a power of nothing greater than 1 is linear.
500
Write two relations:
- Function -
- No Function -
Check student answers
500
A swimming pool that has a shallow end that has a depth of 3 feet and a deep end that has a depth of 8 feet is being filled. When the pool is being filled, the water first fills the entire deep end and then levels out until the entire pool is filled. A graph of the amount of time it takes to fill the pool is shown, where the x-axis represents the time, in minutes, it takes to fill the pool and the y-axis represents the depth of the water in the pool from the bottom of the deep end.
Enter the amount of minutes it will take before the water starts to flow into the shallow end.
60 minutes. Find 3 on the y axis and match it to the minutes on the x axis.
500
What is function notation?
A way of writing functions using symbols like f(x).
500
The equation y = x + 1 defines the relationship between x and y, where x is the input and y is the output.
Which statements about the graph of this relationship are true? Select two that apply.
A.) graph is curved. B.) graph is a straight line
C.) The graph is vertical. D.)Graph is a function
B and D
500
f(x) = 3x + 5
solve: f(-2) f(6) f(0)
f(-2)= -1
f(6) = 23
f(0)= 5