Unit 6, Lesson 6
Connecting Representations of Functions
Accelerated 7
6.1
Warm-up
Here are three different ways of representing functions. How are they alike? How are they different?
| -2 | -1 | 0 | 1 | 2 | 3 | |
| 4 | 2 | 0 | -2 | -4 | -6 |
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Here are three different ways of representing functions. How are they alike? How are they different?
| -2 | -1 | 0 | 1 | 2 | 3 | |
| 4 | 2 | 0 | -2 | -4 | -6 |
The graph shows the temperature between noon and midnight in City A on a certain day.
Graph in a coordinate plane, horizontal, time in hours after noon, 0 to 12 by ones, vertical, temperature in degrees Farenheit, 50 to 60 by ones. The graph starts at 0 comma 50 and climbs slowly, the more quickly as it moves right, going through 2 comma 52 and 4 comma 57 before peaking at 5 point 8 comma 59. The graph then steadily declines as it moves right until it reaches the point 12 comma 52 point 5.
The table shows the temperature, , in degrees Fahrenheit for hours after noon in City B.
| 1 | 2 | 3 | 4 | 5 | 6 | |
| 82 | 78 | 75 | 62 | 58 | 59 |
The volume, , of a cube with edge length cm is given by the equation .
The volume of a sphere is a function of its radius (in cm), and the graph of this relationship is shown here.
Functions are all about getting outputs from inputs. For each way of representing a function—equation, graph, table, or verbal description—we can determine the output for a given input.
Let’s say we have a function represented by the equation , where is the dependent variable and is the independent variable. If we wanted to find the output that goes with 2, we could input 2 into the equation for and find the corresponding value of . In this case, when is 2, is 8 since .
If we had a graph of this function instead, then the coordinates of points on the graph would be the input-output pairs.
So we would read the -coordinate of the point on the graph that corresponds to a value of 2 for . Looking at the following graph of a function, we can see the point on it, so the output is 8 when the input is 2.
The graph of a line in the coordinate plane with the origin labeled “O”. The horizontal axis has the numbers negative 1 through 2 indicated and there are vertical gridlines between each integer. The vertical axis has the numbers negative 2 through 8, in increments of 2, indicated, and there are horizontal grid lines in between each integer. The line begins to the right of the y axis and below the x axis. It slants upward and to the right passing through the point with coordinates negative 1 comma negative 1, crosses the y axis at 2, and passes through the indicated point labeled 2 comma 8.
A table representing this function shows the input-output pairs directly (although only for select inputs).
Again, the table shows that if the input is 2, the output is 8.
| -1 | 0 | 1 | 2 | 3 | |
| -1 | 2 | 5 | 8 | 11 |