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Q73.

Expert-verifiedFound in: Page 530

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Graph the pair of functions $y={\left(\frac{1}{5}\right)}^{x}\u200a\text{and}y={\left(\frac{1}{5}\right)}^{x-2}$**** 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 $y=25$.

The given functions are $y={\left(\frac{1}{5}\right)}^{x}\u200a\text{and}y={\left(\frac{1}{5}\right)}^{x-2}$.

The graph of the functions on the same functions on the same screen is shown below.

**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 $y=25$.

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