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(x)=12f(x)+1 is B

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Expert Answer

Asma Vang
Answered 2021-02-20 Author has 93 answers

Vertical translation:
For b > 0,
The graph of y=f(x) + b is the graph of y=f(x) {shifted up b units}
The graph of y=f(x)  b is the graph of y=f(x) + b {shifted down b units}
Reflection:
Across the x-axis:
The graph of y= f(x) is the reflection of the graph of y=f(x) across the x-axis
Across the y-axis:
The graph of y= f(x) is the reflection of the graph of y=f(x) across the x-axis
Vertically Stretching or Shrinking:
The graph of y= af(x) can be obtained from the graph of y=f(x) by
Stretching verttically for midamid > 1 or shrinking vertically for a > midamid > 1.
For a<0, the graph is also reflected across the x-axis
. By the properties of transformation, the graph of g(x)=12f(x)+1 is,
The transformation of y=f(x) and shri
vertically by a factor of 12
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(x)=12f(x)+1 is B

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