Question

Use transformations to sketch the graph of the function. s(x)=1 + 0.5^{x}

Transformations of functions
ANSWERED
asked 2020-11-06
Use transformations to sketch the graph of the function. \(\displaystyle{s}{\left({x}\right)}={1}\ +\ {0.5}^{{{x}}}\)

Answers (1)

2020-11-07

Step 1
\(\displaystyle{s}{\left({x}\right)}={1}\ +\ {0.5}^{{{x}}}={1}\ +\ {\left(\frac{{1}}{{2}}\right)}^{{{X}}}={1}\ +\ {2}^{{-{x}}}\)
Remember that: When we reflect the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) in the y-axis, we get the graph for \(\displaystyle{y}={f{{\left(-{x}\right)}}}\)
We will start the graph of the standard function \(\displaystyle{y}={2}^{{{x}}}\) (represented by blue dashed curve)
Reflect the graph of \(\displaystyle{y}={2}^{{{x}}}\) in the y-axis, to get the graph for \(\displaystyle{y}={2}^{{-{x}}}\) (represented by black solid curve)
image
Step 2
Remember that: When we shift the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) by k units upwards, we get the graph for \(\displaystyle{y}={f{{\left({x}\right)}}}\ +\ {k}\)
Shift the graph of \(\displaystyle{y}={2}^{{-{x}}}\) by 1 unit upwards, to get the graph for \(\displaystyle{y}={1}\ +\ {2}^{{-{x}}}\) (represented by red solid curve).
The graph for \(\displaystyle{y}={2}^{{-{x}}}\) is represented by black dashed curve.
image

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