Function Transformation Math Example 4

Follow the full solution, then compare it with the other examples linked below.

hard

Write the equation of the function obtained by reflecting

f(x)=\log_2(x)

over the

y

-axis, compressing horizontally by a factor of

3

, and shifting up

5

1
Reflect over $y$ -axis: replace $x$ with $-x$ → $\log_2(-x)$ .
2
Compress horizontally by factor $3$ (multiply argument by $3$ ): $\log_2(-3x)$ . Shift up $5$ : add $5$ outside → $g(x) = \log_2(-3x) + 5$ . Domain: $-3x > 0 \Rightarrow x < 0$ .

Answer

g(x) = \log_2(-3x) + 5

, domain

x < 0

Reflections and compressions affect the argument of the function. Applying the reflection first (

-x

) then the horizontal compression (

-3x

) gives the correct combined transformation. The shift is applied last, outside the function.

About Function Transformation

A function transformation shifts, stretches, compresses, or reflects the graph of a parent function by modifying its formula in a systematic way.

Describe all transformations applied to [formula] to obtain [formula].

Starting from [formula], apply the transformation [formula] step by step and identify the key point

The graph of [formula] passes through [formula]. Where does the transformed graph [formula] pass thr