one point which must be on the graph of each of the following functions.

Question

the point (7,4) is on the graph of y=g(x) give the coordinates of one point which must be on the graph of each of the following functions.

 

1/4 g(x) 

g(1/4x)

-g(4x)

-4 g(x)

Answer 1

We have g(7)=4.

 

Define f₁(x) =1/4 g(x). Then f₁(7)=1/4 g(7) =1, so (7,1) is on the graph of f₁.

 

Define f₂(x) = g(1/4 x). Then f₂(28)= g(7) =4, so (28,4) is on the graph of f₂.

 

Define f₃(x) =-g(4x). Then f₃(7/4)= -g(7) =-4, so (7/4,-4) is on the graph of f₃.

 

Define f₄(x) =-4 g(x). Then f₄(7)=-4 g(7) =-16, so (7,-16) is on the graph of f₄.