Graph the pair of functions $y = {(\frac{1}{5})}^{x} and y = {(\frac{1}{5})}^{x - 2}$ on the same screen. Then compare the graphs, listing both similarities and differences in shape, asymptotes, domain, range and y-intercept.

Question

Graph the pair of functions $y = {(\frac{1}{5})}^{x} and y = {(\frac{1}{5})}^{x - 2}$ on the same screen. Then compare the graphs, listing both similarities and differences in shape, asymptotes, domain, range and y-intercept.

Accepted Answer

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 $y = {(\frac{1}{5})}^{x}$ is $y = 1$ and the y-intercept of $y = {(\frac{1}{5})}^{x - 2}$ is $y = 25$ .

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Algebra 2

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Short Answer

Graph the pair of functions $y = {(\frac{1}{5})}^{x} and y = {(\frac{1}{5})}^{x - 2}$ on the same screen. Then compare the graphs, listing both similarities and differences in shape, asymptotes, domain, range and y-intercept.

Step by Step Solution

Step 1. Write down the given equation.

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

Step 3. Interpretation from the graph of two functions.

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Algebra 2

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Graph the pair of functions y=15x and y=15x-2 on the same screen. Then compare the graphs, listing both similarities and differences in shape, asymptotes, domain, range and y-intercept.

Step by Step Solution

Step 1. Write down the given equation.

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

Step 3. Interpretation from the graph of two functions.

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Graph the pair of functions $y = {(\frac{1}{5})}^{x} and y = {(\frac{1}{5})}^{x - 2}$ on the same screen. Then compare the graphs, listing both similarities and differences in shape, asymptotes, domain, range and y-intercept.