Question

Which of the following transformations are used when transforming the graph of the parent function (x) = logs x to the graph of g(x)--2 log,(x-6) ? Select all that apply.

a. Shift the graph of(x) 6 units down.
b. Shift the graph off (x) 6 units to the left.
c. Reflect the graph of /(x) over the x-axis.
d. Stretch the graph of,f(x) vertically by a factor of 2.
e. Stretch the graph of f(x) vertically by a factor of -1/-2

Answer 1

The graph of function g(x) = 2log(x - 6) is obtained by shifting the graph of f(x) = log(x) 6 units to the right and stretching it vertically by a factor of 2. Option D is correct.

Step-by-step explanation:

The question asks which transformations apply when transforming the graph of the parent function f(x) = log(x) to the graph of g(x) = 2log(x - 6). To understand this, we'll consider the transformations step by step.

The term -6 inside the logarithm indicates a horizontal shift, but contrary to what might be intuitive, it actually shifts the graph 6 units to the right, not to the left. That is because the function moves in the opposite direction to the sign inside the function.

The coefficient 2 in front of the logarithm implies a vertical stretch by a factor of 2. This means that for any given x-value, the y-value of g(x) will be twice that of f(x).

In conclusion, the correct transformations are a horizontal shift to the right by 6 units and a vertical stretch by a factor of 2.

The graph of the parent function (x) = log(x) can be transformed to the graph of g(x) = -2log(x-6) by applying the following transformations:

Shift the graph of (x) 6 units to the right: This means that every x-coordinate is increased by 6.

Stretch the graph of (x) vertically by a factor of -2: This means that the y-coordinate is multiplied by -2, which reflects the graph over the x-axis and flips it vertically.