describe a function ( g(x) ) in terms of ( f(x) ) if the graph of ( g ) is obtained by reflecting the graph…

describe a function ( g(x) ) in terms of ( f(x) ) if the graph of ( g ) is obtained by reflecting the graph of ( f ) about the ( x )-axis and if it is horizontally stretched by a factor of 8 when compared to the graph of ( f ). ( g(x)=a f(b x)+c ) where ( a = ) ( b = -\frac{1}{8} ) ( c = 0 )

describe a function ( g(x) ) in terms of ( f(x) ) if the graph of ( g ) is obtained by reflecting the graph of ( f ) about the ( x )-axis and if it is horizontally stretched by a factor of 8 when compared to the graph of ( f ). ( g(x)=a f(b x)+c ) where ( a = ) ( b = -\frac{1}{8} ) ( c = 0 )

Answer

Explanation:

Step1: Reflect about the x - axis

When reflecting a function (y = f(x)) about the (x) - axis, the transformation is (y=-f(x)). In the form (g(x)=Af(Bx)+C), this means (A=- 1).

Step2: Horizontal stretch

For a horizontal stretch of a function (y = f(x)) by a factor (k), the transformation is (y = f\left(\frac{x}{k}\right)). Here, (k = 8), so (B=\frac{1}{8}).

Step3: Check for vertical shift

Since there is no vertical shift mentioned, (C = 0).

Answer:

(A=-1), (B=\frac{1}{8}), (C = 0)