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Expert-verified Found in: Page 530 ### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903 # Graph the pair of functions $y={\left(\frac{1}{5}\right)}^{x} \text{and}y={\left(\frac{1}{5}\right)}^{x-2}$ on the same screen. Then compare the graphs, listing both similarities and differences in shape, asymptotes, domain, range and y-intercept.

The shape of the two graphs is same. The asymptote of the both functions is horizontal $y=0$. The domain of both the functions is the set of all real numbers (R). The range of the both functions is $y>0$. The y-intercept of $y={\left(\frac{1}{5}\right)}^{x}$ is $y=1$ and the y-intercept of $y={\left(\frac{1}{5}\right)}^{x-2}$ is $y=25$.

See the step by step solution

## Step 1. Write down the given equation.

The given functions are $y={\left(\frac{1}{5}\right)}^{x} \text{and}y={\left(\frac{1}{5}\right)}^{x-2}$.

## Step 2. Sketch the graphs of the functions on the same screen.

The graph of the functions on the same functions on the same screen is shown below. ## Step 3. Interpretation from the graph of two functions.

• Shape: The shape of the two graphs are of smooth curve and they are of same shape.
• Asymptotes: The asymptote of the function $y={\left(\frac{1}{5}\right)}^{x}$ is horizontal $y=0$, whereas the asymptote of $y={\left(\frac{1}{5}\right)}^{x-2}$ is $y=0$.
• Domain: The domain of both the functions is the set of all real numbers (R).
• Range: The range of the function $y={\left(\frac{1}{5}\right)}^{x}$ is $y>0$, and the range of $y={\left(\frac{1}{5}\right)}^{x-2}$ is $y>0$.
• y-intercept: From the graph it can be seen that the y-intercept of $y={\left(\frac{1}{5}\right)}^{x}$ is $y=1$ and the y-intercept of $y={\left(\frac{1}{5}\right)}^{x-2}$ is $y=25$. ### Want to see more solutions like these? 