MATH SOLVE

4 months ago

Q:
# The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units. Choose the correct function to represent the transformation

Accepted Solution

A:

Answer:The required function is [tex]g(x)=\frac{1}{2}(5^{x-3})-2[/tex].Step-by-step explanation:The given parent function is[tex]f(x)=5^x[/tex]The transformation of a parent function is defined as[tex]g(x)=kf(x+a)+b[/tex]Where, k represents the vertical stretch or compression, a represents the horizontal shift and b represent the vertical shift.β If |k|>1, then it represents vertically stretch and If |k|<1, then it represent vertically compression.β If a>0, then f(x) shifts left by a units and If a<0, then f(x) shifts right by a units.βIf b>0, then f(x) shifts upward by b units and If b<0, then f(x) shifts downward by b units.Since the graph of f(x) has been vertically compressed by a factor of one-half shifted to the right three units and down two units. [tex]k=\frac{1}{2}[/tex][tex]a=-3[/tex][tex]b=-2[/tex]The graph of required function is[tex]g(x)=\frac{1}{2}f(x-3)-2[/tex][tex]g(x)=\frac{1}{2}(5^{x-3})-2[/tex]Therefore the required function is [tex]g(x)=\frac{1}{2}(5^{x-3})-2[/tex].