Question

Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) = 2logx + 6 A.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up. B.) The graph of g(x) is the graph of f(x) reflected in the x-axis, expanded vertically by a factor of 2, and translated 6 unit(s) up. C.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) down. D.) The graph of g(x) is the graph of f(x) reflected in the x-axis, expanded vertically by a factor of 2, and translated 6 unit(s) down.

Answer 1

Answer:

  A.)  The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.

Step-by-step explanation:

For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...

  g(x) = k·f(x)

For translation up by k units, f(x) is transformed to ...

  g(x) = f(x) +k

___

Comparing the following ...

  f(x) = log(x)

  g(x) = 2·log(x) +6

We see that a multiplication factor and an addition factor have been applied. That means ...

  g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.