7.1.4 The Input and Output of a Function
7.1.4 • The Input and Output of a Function
Cool Down
A rectangularyard is enclosed by 100 meters of fencing. The table shows some possible values for the length and width of the yard.
| Length (meters) | Width (meters) | Area (square meters) |
|---|---|---|
| 10 | 40 | 400 |
| 20 | 30 | |
| 25 | 25 | 625 |
| 35 | 15 | 525 |
| 40 |
Complete the table with the missing values.
Compare your answer:
| Length (meters) | Width (meters) | Area (square meters) |
|---|---|---|
| 10 | 40 | 400 |
| 20 | 30 | 600 |
| 25 | 25 | 625 |
| 35 | 15 | 525 |
| 40 | 10 | 400 |
The missing value in the second row is 600. The missing values in the last row are 10 and 400.
If the values for length and area are plotted, what would the graph look like?
Compare your answer:
The points would form a stretched out upside-down U shape, or an arch.
How is the relationship between the length and the area of the rectangle different from other kinds of relationships we’ve seen before?
Compare your answer:
As one quantity increases, the other quantity first increases and then decreases, instead of always increasing or always decreasing.