Question

Consider the line y = x . If the line is dilated by a factor of 2, what is the equation of the resulting line? If the resulting line is translated 3 units up, what is the equation of the resulting line?

Answer 1

Remember, if f(x) is a function, then

1. We can move up or down f(x) adding a constant c to the whole function, that is, f(x)+c is the function f(x) translated c units up if c is positive or c units down if c is negative.

2. We can compress or dilate f(x) multiplying the whole function by a factor c, that is, cf(x) is the function dilated by a factor of c if
`c\geq 1` or cf(x) is he function compress by a factor of c if
`0<c<1`.

Then, if y=f(x)=x

1. The equation of f(x) dilated by a factor of 2 is
`g(x)=2f(x)=2x`

2. The equation of f(x) translated 3 units up is
`g(x)=f(x)+3=x+3`