A.1.D.10.7TN
Answer to Problem 7:
y = 3x is a linear function and y = 3x is an exponential function. Linear functions have a constant rate of change while exponential functions have varying rates of change. The linear equation, y = 3x has a constant rate of change of 3 (as x increases by 1, y increases by 3). The exponential function has a varying rate of change. The rates of change depend upon the value of x and the function. The domain and range of y = 3x is domain {x: x Î Â } (all real numbers) and range {y: y Î Â}(all real numbers). The domain and range of y = 3x is domain {x: x Î Â} (all real numbers) and range {y: y > 0}.
|
x |
-6 |
-5 |
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
3x |
-18 |
-15 |
-12 |
-9 |
-6 |
-3 |
0 |
3 |
6 |
9 |
12 |
15 |
18 |
|
3x |
0.00137 |
0.00412 |
0.01235 |
0.03704 |
0.11111 |
0.33333 |
1 |
3 |
9 |
27 |
81 |
243 |
729 |
Teacher Notes:
Students will identify y = 3x as a linear equation and one that has a constant growth of 3, with each increase of x by 1, y will increase by 3. y = 3x is a straight line. y = 3x is exponential, as x increases by 1, y will triple. With each change in the x value the y value will change by 3 times the previous y value. This will not be a straight-line graph. As x becomes negative (moving right to left) for the first equation it will continue to decrease (since moving from right to left) by 3. y = 3x will have a y value that will get closer and closer to (or approach) zero, but not equal zero.