Question

Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) =

Answer 1

The transformation that results in the graph of g is: B. The graph of g(x) is the graph of f(x) reflected in the x-axis, expanded vertically by a factor of 5, and translated 8 unit(s) down.

In Mathematics and Geometry, a reflection over or across the x-axis or the line y = 0 can be represented by the following transformation rule (x, y) → (x, -y).

By critically observing the parent logarithmic function f(x) = logx, we can reasonably and logically deduce that it was reflected over the x-axis, followed by a vertical stretch (expansion) using a factor of 5, and then vertically translated 8 units down, in order to produce the graph of the transformed logarithmic function g(x);

g(x) = -bf(x) - k

g(x) = -5f(x) - 8

g(x) = -5logx - 8

Answer 2

Hey there!

Answer:

2nd choice, The graph of g(x) is the graph of f(x) reflected in the x-axis, expanded vertically by a factor of 5, and translated 8 unit(s) down.

Explanation:

Recall that the transformation form of a logarithmic function is:

y = ±alog(b(x-h))+k

Given g(x) = -5logx-8:

Negative in front of equation: reflection over the x-axis

'a' value of 5: expanded vertically by a factor of 5

'k' value of -8: translated 8 unit(s) down.