Question

Describe the transformation of the graph from f(x) to g(x)

1) f(x)=2x+1
g(x)=2x+4

2) f(x)=x+3
g(x)=-x+1

3) f(x)=x^2
g(x)=(x-1)^2 +3

Answer 1

1) f(x)=2x+1
g(x)=2x+4

For 1, the line is being shifted up 3 units on the y axis. We can see this in image 1. The orange line is f(x) and the purple is g(x).

2) f(x)=x+3
g(x)=-x+1

For number 2, the line is being shifted down 2 units on the y axis and being transformed perpendicular to f(x) We can see this in image 2. The black line is f(x) and the red is g(x)

3) f(x)=x^2
g(x)=(x-1)^2 +3

For number 3, the equation is being shifted to the left. When we subtract a number form x like (x-1) it shifts the equation to the right by the number that is being subtracted. When we add a number like the 3 in (x-1)^2 +3, it shift the equation up 3 units. We can see this in the 3rd image. The blue line is f(x) and the green line is g(x)