# Determining Equation from Graph?

I'll repost this again.

Given the graph of y=log_2(x) and the point (8,1) & (1,0). I'm given a mystery graph with no equation but I'm given the points (1,0) and (8,4). How do I find the vertical stretch factor/translation?

### 1 Answer

- Wayne DeguManLv 71 month ago
You imply that points (8, 1) and (1, 0) are on the curve y = log₂x

I agree that (1, 0) is on the curve as 0 = log₂(1)

However, 1 ≠ log₂(8)

Now, log₂(8) = 3, hence point (8, 3) would be on the curve.

That aside, you are saying that points (8, 1) and (1, 0) are transformed to (8, 4) and (1, 0)

A vertical stretch multiplies the vertical co-ordinates

Hence, 1 x 4 = 4 and 0 x 4 = 0

so, vertical stretch is 4

so, y = log₂x is transformed to y = 4log₂x

Below is a sketch showing how (8, 3) and (1, 0) are transformed to (8, 12) and (1, 0), illustrated by log₂x in red and 4log₂x in blue

Note, points (2, 1) and (4, 2) are transformed to (2, 4) and (4, 8)...i.e. vertically by a factor of 4

:)>