Exercise 64 Page 315

We will graph the given function using a graphing calculator. Then, we will determine the domain, range, and asymptote of the function.

Graphing the Function

To draw a graph on a calculator, we first press the $\boxed{\text{Y}=}$ button and type the function in one of the rows. To type a logarithmic function, we use the $\boxed{\text{LOG}}$ button. Having written the function, we can push $\boxed{\text{GRAPH}}$ to draw it.

Domain, Range, and Asymptote

Let's recall the function again! Note that, considering the real numbers, we can take a logarithm of a positive number only. Therefore, we know that $x$ needs to be greater than $0.$ From here, we can conclude that the domain of the function is the set of all real numbers greater than $0.$ Notice that also in the graph, as $x$ approaches $0,$ the function approaches positive infinity. Therefore, there is a vertical asymptote at $x=0.$ Since there is no restriction on the values of $y,$ the range is the set of all real numbers.