how do you graph the function...
f(x)=2^x over the interval -2 is less than or equal to x is less than or equal to 3.
Help please! THANKS!
To graph the function f(x) = 2^x over the interval -2 ≤ x ≤ 3, you can follow these steps:
1. Identify the interval: The given interval is -2 ≤ x ≤ 3, which means x values range from -2 to 3 (inclusive).
2. Determine the y-values: Substitute different x-values within the given interval (-2 to 3) into the function f(x) = 2^x to find the corresponding y-values.
For example:
- When x = -2, y = 2^-2 = 1/4 = 0.25
- When x = -1, y = 2^-1 = 1/2 = 0.5
- When x = 0, y = 2^0 = 1
- When x = 1, y = 2^1 = 2
- When x = 2, y = 2^2 = 4
- When x = 3, y = 2^3 = 8
3. Plot the points: On a graph, mark the corresponding points (x, y) that you found in the previous step. Connect the dots to visualize the graph.
- (-2, 0.25)
- (-1, 0.5)
- (0, 1)
- (1, 2)
- (2, 4)
- (3, 8)
4. Draw the curve: Connect the marked points smoothly to form a curve. In this case, the function f(x) = 2^x is an exponential function, so the curve will be increasing rapidly as x moves to the right.
5. Label the axes: Label the x-axis and y-axis appropriately to indicate the values represented.
Example labels: x-axis: -2, -1, 0, 1, 2, 3; y-axis: 0.25, 0.5, 1, 2, 4, 8
That's it! You have successfully graphed the function f(x) = 2^x over the interval -2 ≤ x ≤ 3.