 # To determine.The correct graph for the function[g(x)=-frac{1}{2}f(x)+1 is B ringearV 2021-02-19 Answered

To determine.
The correct graph for the function $g\left(x\right)=-\frac{1}{2}f\left(x\right)+1$ is B

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Vertical translation:
For ,
The graph of is the graph of $y=f\left(x\right)$ {shifted up b units}
The graph of is the graph of {shifted down b units}
Reflection:
Across the x-axis:
The graph of is the reflection of the graph of $y=f\left(x\right)$ across the x-axis
Across the y-axis:
The graph of is the reflection of the graph of $y=f\left(x\right)$ across the x-axis
Vertically Stretching or Shrinking:
The graph of can be obtained from the graph of $y=f\left(x\right)$ by
Stretching verttically for or shrinking vertically for .
For $a<0$, the graph is also reflected across the x-axis
. By the properties of transformation, the graph of $g\left(x\right)=-\frac{1}{2}f\left(x\right)+1$ is,
The transformation of $y=f\left(x\right)$ and shri
vertically by a factor of $\frac{1}{2}$
Then the graph is reflection about the x-axis and shifted up one unit.
From the given graphs, the graphs B satisfies the all condition's stated above.
Thus, the correct graph for the function $g\left(x\right)=-\frac{1}{2}f\left(x\right)+1$ is B