Question

Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 3, reflected across the x-axis, and shifted 7 units to the right.

Answer 1

ANSWER

$y = - 3 ln(x - 7)$

EXPLANATION

The given logarithmic function is

$f(x) = ln(x)$

The transformation,

$y = - cf(x - k)$

stretches the graph of y=f(x) vertically by a factor of c units.

The graph is also shifted to the right by k, units.

The negative sign reflects y=f(x) in the x-axis.

Hence, the transformed function that represents f(x) = ln x stretched vertically by a factor of 3, reflected across the x-axis, and shifted 7 units to the right

$y = - 3 ln(x - 7)$