Function Notation
Let f(x)=x+3
Find f(5)=_____
What is 8?
A student receives a fixed allowance of $3. The amount of money they does not change over time.
Create a graph that represents the amount of money y the student has after x days.
What is a horizontal line at y=3?
What is "average rate of change" asking you to do
What is finding the distance between two points?
A graph shows the total number of pages read over time. The graph is a straight line that starts at 0 pages when time is 0 hours and goes steadily up.
Explain what the graph tells you about how the person is reading.
What is
- The graph represents a function
- Constant rate
- Reading speed is steady
- As time increases, pages increase
A graph shows money earned based on hours worked. The graph crosses the y-axis at 0.
What does the y-intercept mean in this situation
What is starting value or money earned before working?
g(x)=4x-1
Find g(-7)=____
What is -29?
At the start of the day, a student already ahs 1 unread text message. They receive 2 new text messages every hour.
Graph the number of unread messages y after x hours.
What is y=2x+1?
Find the difference between (0,4) and (16,20)
What is 1?
The function d(t)=60t represents the distance (in miles) traveled after t hours.
Explain what d(3)=180 means in words.
What is after 3 hours, the distance traveled is 180 miles?
A graph shows the amount of gas left in a car over time. The graph is decreasing.
Explain what it means that the graph is decreasing.
What is, as time increases, gas decreases?
Let D(k)=3/9k
Find D(4)=____
What is 1.3?
A video game character starts with 4 lives. Each time they lose a level, they lose 1 life.
Graph the number of lives y remaining after x levels are lost.
What is y=-x+4?
y=6x+10. Find the average rate of change.
What is 6?
Two students ride bikes after school.
- Student A's distance graph is a straight line, y=4x
- Student B's distance curves upward, getting steeper over time, y=x^2
Explain how the students' speeds compare over time
What is
- Straight line = constant speed
- Curved graph = changing speed
- Student B is speeding up
Two lines represent the distance two runners travel over time. One line is steeper than the other.
Explain what the steeper line tells you about the runner.
What is faster speed?
Let H(p)=12p+75. When p=2. Then H(p)=___
What is 99?
A phone has two different features being tracked at the same time.
- The maximum music volume on the phone is set at 4 units and does not change,
- The phone's battery starts 1 unit and drains quickly, losing 2 units every hour while music us playing.
Let x represent time in hours and y represent the amount of each feature.
1) graph both situations on the same coordinate plane.
2) explain in words what each graphs represents.
What is
Music volume: y=4
Phone battery: y=-2x+1
The average rate of change for 30x+15y=45
What is -2?
A plant's height is recorded over several weeks.
At week 2 it is 10 inches tall.
At week 6 it is 18 inches tall.
Explain what the average rate of change represents in this situation.
What is
- Change in output over change in input
- Units (inches per week)
A graph shows the height of a basketball shot over time. The graph reaches a highest point and then falls.
Explain what the highest point on the graph represents.
What is ball stops rising?
or
What is maximum value?
Let B(p)=16p+64. When B(p)=20. Then p=____
What is -2.75?
Two cyclists start at the same elevation on a trail that is 2 feet below sea level.
- Cyclist A is riding uphill and gains 3 feet of elevation each minute.
- Cyclist B is riding downhill and loses 1 foot of elevation each minute.
Let x represent time in minutes and y represent elevation (in feet). Graph on the same plane: y=3x-2 and y=-x-2
What is
y=3x-2
y=-x-2
f(x)=x^2. Let a=1, b=3. Compute f(1) and f(3). Find the average rate of change.
What is 4?
The function h(t) represents the height of a ball (in feet) after t seconds. The graph rises, reaches a maximum, and then falls back to the ground.
Explain what is happening to the ball, and describe the average rate of change before and after the highest point.
What is
- Understanding a non-linear function
- Positive vs negative average rate of change
A function models the number of people in a movie theater over time. The graph continues downward into negative values.
Explain why part of the graph does not make sense in this situation.
What is there can't be negative people?