+180 If (x, y) is on the graph of f(x)=log₁₀(x), state the coordinates (in terms of x and y) that would be on the graph of f(x)=2log₁₀(x-4)+3.
+180 I think I figured it out.
Transformations of f(x)=log₁₀(x) -> f(x)=2log₁₀(x-4)+3
Vertical stretch: f(x)=log₁₀(x) -> f(x)=2log₁₀x
Horizontal translation: f(x)=2log₁₀x -> f(x)=2log₁₀(x-4)
Vertical translation: f(x)=2log₁₀(x-4) -> f(x)=2log₁₀(x-4)+3
In terms of x and y, the vertical stretch and vertical translation would affect y, and the horizontal translation would affect x. Therefore, it would be (x+4, 2y+3).
This can be checked by using the point (1, 0) on :
(1+4, 2(0)+3)
= (5, 3)
(5, 3) is a point on the graph f(x)=2log₁₀(x-4)+3.
