State the parent function, transformations, domain and range. 19610701771.jpg

kzae220o3 2021-11-23 Answered
State the parent function, transformations, domain and range.
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Expert Answer

hotcoal3z
Answered 2021-11-24 Author has 1414 answers
Step 1
Given, \(\displaystyle{f{{\left({x}\right)}}}={2}^{{{\left({x}-{3}\right)}}}+{2}\)
The graph of f(x) is as shown :
image
Step 2
Parent function:\(\displaystyle{2}^{{{x}}}\)
Transformation :
1.Right shift by 3
2.Vertical shift of +2
Domain, D:\(\displaystyle{\left(-\infty,\infty\right)}\)
\(\displaystyle\lim_{{{X}\rightarrow-\infty}}{f{{\left({x}\right)}}}=\lim_{{{x}\rightarrow-\infty}}{\left({2}^{{{x}-{3}}}+{2}\right)}={2}\)
\(\displaystyle\lim_{{{X}\rightarrow\infty}}{f{{\left({x}\right)}}}=\lim_{{{x}\rightarrow\infty}}{\left({2}^{{{x}-{3}}}+{2}\right)}=\infty\)
Range,R:\(\displaystyle{\left[{2},\infty\right)}\)
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