Exercise 50 Page 257

We want to write a rule for g that represents the indicated transformations of the graph of f. f(x)=sqrt(x^2+10x), g(x)=1/4f(- x)+6 To do so, we should first find f(- x) by substituting - x for x into f. f(x)=sqrt(x^2+10x) ⇓ f( - x)=sqrt(( - x)^2+10( - x)) Now we can simplify the above expression.

f(- x)=sqrt((- x)^2+10(- x))

NegBaseToPosBase

(- a)^2=a^2

f(- x)=sqrt(x^2+10(- x))

MultPosNeg

a(- b)=- a * b

f(- x)=sqrt(x^2-10x)

Finally, we will substitute sqrt(x^2-10x) for f(- x) into g(x)= 14f(- x)+6. g(x)=1/4f(- x)+6 ⇓ g(x)=1/4 sqrt(x^2-10x)+6