Q7. - Algebra 2

Question

Sketch the graph of the function $y=2{\left(\frac{1}{3}\right)}^x$. Then state the function’s domain and range.

Step-by-Step Solution

Answer

The domain of the function $y=2{\left(\frac{1}{3}\right)}^x$ is $\left(-\infty ,\infty \right)$ and range is $\left(0,\infty \right)$ whose graph is shown below.

Step 1. Write down the given information.

The given function is $y=2{\left(\frac{1}{3}\right)}^x$.

Step 2. Sketch the graph for the given function.

The graph for the function $y=2{\left(\frac{1}{3}\right)}^x$ using the graphing calculator is shown below.

Step 3. Interpretation from the graph.

From the graph it can be seen that,

x can take all the values from $-\infty \text{ to }\infty$ and y takes all the positive values from $0\text{ to }\infty$ excluding 0. 

Therefore, the domain of the function $y=2{\left(\frac{1}{3}\right)}^x$ is $\left(-\infty ,\infty \right)$ and range of the function is$\left(0,\infty \right)$.