Question

In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x)=log(x) to achieve the graph of g(x)=log(−3x/9)+4. Explain how the parent function is modified to obtain the new function.

Answer 1

The graph of g(x) = log(-3x/9) + 4 is derived from the parent function f(x) = log(x) through a combination of horizontal compression, horizontal reflection, and vertical shift.

Step-by-step explanation:

The graph of the function g(x) = log(-3x/9) + 4 is derived from the parent function f(x) = log(x) through a combination of transformations.

1. Horizontal compression: The coefficient of x, which is -3 in this case, causes a horizontal compression by a factor of 1/3. This means that the graph of g(x) will be narrower than the graph of f(x).

2. Horizontal reflection: The negative sign in front of the x term in -3x reflects the graph of g(x) across the y-axis. This means that the graph of g(x) will be a mirror image of the graph of f(x) with respect to the y-axis.

3. Vertical shift: The +4 term in the function causes a vertical shift of 4 units upward. This means that the graph of g(x) will be shifted 4 units higher than the graph of f(x).