+0  
 
0
24
1
avatar+172 

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.

 Jan 11, 2023
 #1
avatar+172 
0

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. 

 Jan 11, 2023

17 Online Users