Question

4. The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 1

Function
`f(x)` is shifted 1 unit left and 1 unit up.

`f(x)\rightarrow f(x+1)+1`

Transformed function
`f(x+1)+1=\log(x+1)+1`

Explanation:

Given:

Red graph (Parent function):

`f(x)=\log(x)`

Blue graph (Transformed function)

From the graph we can see that the red graph is shifted 1 units left and 1 units up.

Translation Rules:

`f(x)\rightarrow f(x+c)`

If
`c>0` the function shifts
`c` units to the left.

If
`c<0` the function shifts
`c` units to the right.

`f(x)\rightarrow f(x)+c`

If
`c>0` the function shifts
`c` units to the up.

If
`c<0` the function shifts
`c` units to the down.

Applying the rules to
`f(x)`

The transformation statement is thus given by:

`f(x)\rightarrow f(x+1)+1`

As function
`f(x)` is shifted 1 unit left and 1 unit up.

Transformed function is given by:

`f(x+1)+1=\log(x+1)+1`