Functions & Relations
What is a function?
A function is a relation where each input (x-value) has exactly one output (y-value).
What does it mean for a function to be linear?
A linear function has a constant rate of change and forms a straight line when graphed.
What is the rate of change also called?
Slope
What does the y-intercept represent in a real-world situation?
The y-intercept represents the starting value or initial amount.
What winter sport did Ms. Hunter do when she was little?
Skiing
Does the set of ordered pairs (0,2), (2,0), (2,2), (3,4) represent a function? Why or why not?
No, it is not a function because the x-value 2 is paired with two different y-values (0 and 2).
A table shows x increases by 3 each time and y increases by 5 each time. Is the function linear or nonlinear?
Linear, because y increases by the same amount each time x increases by the same amount.
Find the slope between the points (2,11) and (8,14).
(14-11)/(8-2) = 3/6 = 1/2
Describe what an increasing graph means in a real-life context.
It means the quantity is increasing as time or another variable increases.
What winter job did Ms. Hunter want as a kid?
Avalanche search & rescue (ski patrol)
Which test can you use on a graph to determine whether a relation is a function?
The vertical line test.
How can you tell from a graph whether a function is linear or nonlinear?
A linear graph is a straight line; a nonlinear graph is curved or changes direction.
Which part of the formula y=mx+b represents the rate of change?
The letter m.
A graph shows a flat section. What does this mean about the rate of change?
The rate of change is zero; the value is staying the same.
What is tomorrows spirit day?
Dress as a christmas character
A relation has two points with the same x-value but different y-values. Is it a function? Explain.
No, it is not a function because one input has more than one output.
One function is shown by a straight line, and another is curved. Which one is linear and why?
The straight-line graph is linear because it has a constant rate of change.
Compare two functions and determine which has the greater rate of change.
The function with the larger slope (greater numerical value) has the greater rate of change.
Sketch and describe a graph that represents going uphill, then flat, then downhill over time.
The graph should rise (uphill), then be flat (constant), then fall (downhill).
What are we doing in math class tomorrow?
Taking the unit 3 test
Given a graph with several plotted points, explain how you would justify whether or not the relation is a function.
Check whether any x-value is paired with more than one y-value or whether a vertical line would cross the graph more than once.
A table has a constant rate of change, but the graph is not a straight line. Can it be linear? Explain.
No. If the graph is not a straight line, the function is not linear, even if part of the table appears consistent.
Explain how you can tell whether a slope is positive, negative, or zero by looking at a graph.
A positive slope rises left to right, a negative slope falls left to right, and a zero slope is a horizontal line.
Write a linear equation in the form y=mx+b to represent a situation with a starting fee and a constant hourly rate.
Answers may vary. Example: y=10x+25, where 25 is the starting fee and 10 is the hourly rate.
What is friday?
The last school day before break!