Questions: Graph the logarithmic function (g(x)=log 3(x+3)). To do this, plot two points on the graph of the function, and also draw the asymptote. Then, click on the graph-a-function button. Additionally, give the domain and range of the function using interval notation. Domain: Range:

Graph the logarithmic function (g(x)=log 3(x+3)). To do this, plot two points on the graph of the function, and also draw the asymptote. Then, click on the graph-a-function button. Additionally, give the domain and range of the function using interval notation.

Domain:

Range:

Transcript text: Graph the logarithmic function $g(x)=\log _{3}(x+3)$. To do this, plot two points on the graph of the function, and also draw the asymptote. Then, click on the graph-a-function button Additionally, give the domain and range of the function using interval notation. Domain: $\square$ Range: $\square$

Solution

Solution Steps

Step 1: Identify the asymptote

The function g(x) = log₃(x+3) has a vertical asymptote where the argument of the logarithm is equal to zero. So, x + 3 = 0, which means x = -3.

Step 2: Find two points on the graph

We can find two points by choosing convenient x-values.

If x = -2, then g(-2) = log₃(-2+3) = log₃(1) = 0. So, the point (-2, 0) is on the graph.
If x = 0, then g(0) = log₃(0+3) = log₃(3) = 1. So, the point (0, 1) is on the graph.

Step 3: Determine the domain and range

The domain of a logarithmic function is the set of all x-values for which the argument is greater than zero. In this case, x + 3 > 0, which means x > -3. In interval notation, the domain is (-3, ∞).

The range of a logarithmic function is all real numbers, or (-∞, ∞).