Consider the function: ƒ(x) =(1/2)^x
Graph the exponential function to identify the y-intercept.
Graph the exponential function to identify the end behavior
To graph the function ƒ(x) = (1/2)^x, you can start by evaluating the function at a few different x-values to get some points to plot on a graph.
When x = 0, the function is (1/2)^0 = 1, so the y-intercept is at the point (0, 1).
You can also evaluate the function at a few more x-values to get additional points. For example, when x = 1, the function is (1/2)^1 = 1/2, so the point (1, 1/2) is on the graph. When x = 2, the function is (1/2)^2 = 1/4, so the point (2, 1/4) is on the graph.
You can continue this process to get more points to plot, or you can use a graphing calculator or online graphing tool to quickly plot the points.
As for the end behavior of the function, as x approaches positive infinity, the value of the function approaches 0. This is because as x gets larger and larger, the value of (1/2)^x gets smaller and smaller, approaching 0 but never actually reaching it.
Similarly, as x approaches negative infinity, the value of the function approaches infinity. This is because as x becomes more and more negative, the value of (1/2)^x becomes larger and larger, approaching infinity.
So the end behavior of the function is that it approaches 0 as x approaches positive infinity, and it approaches infinity as x approaches negative infinity.