Aallyah plans to graph the exponential function y=9((2)/(3))^x Mark each statement as true or false. __ a. Aallyah's graph will increase from left to right. __ b. Aallyah's graph will have a y-intercept at (0,9) __ c. As x increases , the y-values on Aallyah's graph will approach 0. __ d. Aallyah's graph will have an asymptote at x=0 __ e. Aallyah's graph will have a x-intercept at ((2)/(3),0)

## Step 1<br />The given function is \(y=9(\frac {2}{3})^{x}\). This is an exponential function. The base \(\frac {2}{3}\), which is less than 1. This means that the function is decreasing.<br /><br />## Step 2<br />The y-intercept of a function is the value of y when x is 0. Substituting x = 0 into the function, we get \(y=9(\frac {2}{3})^{0} = 9\). So, the y-intercept is at (0,9).<br /><br />## Step 3<br />As x increases, the y-values on the graph will approach 0. This is because the base of the exponential function is less than 1, and as x increases, the value of \((\frac {2}{3})^{x}\) decreases, making y approach 0.<br /><br />## Step 4<br />The function does not have an asymptote at x=0. An asymptote is a line that the graph of a function approaches. In this case, the function approaches 0 as x increases, but it does not approach a specific value of x.<br /><br />## Step 5<br />The function does not have an x-intercept at \((\frac {2}{3},0)\). An x-intercept is a value of x for which y is 0. Substituting x = \(\frac {2}{3}\) into the function, we get \(y=9(\frac {2}{3})^{\frac {2}{3}}\), which is not equal to 0.