Standardized Test Practice
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Start by making a table of values and drawing a graph of the given exponential function.
J
We want to determine which of the given values of x would produce a point closest to the x-axis. Let's start by drawing a graph of the given exponential function.
y= 3^x
Because the base of the function is greater than 1, we know that this is an exponential growth function. To draw the graph, we will make a table of values.
| x | 3^x | y=3^x |
|---|---|---|
| - 2 | 3^(- 2) | 1/9 |
| - 1 | 3^(- 1) | 1/3 |
| 0 | 3^0 | 1 |
| 1 | 3^1 | 3 |
| 2 | 3^2 | 9 |
These ordered pairs all lie on the function. Now, we will plot and connect these points with a smooth curve.
Since y= 3^x is an increasing function, the values of y increase when the x-values increase. Moreover, the range of the function is all real values greater than 0. Therefore, the point closest to the x-axis should have the least y-value, which is produced by the least x-value. To check this, let's mark the points with the given x-coordinates.
Now we can see that - 34, produces the point that is closest to the x-axis. Therefore, J is the correct answer.