Question

Describe how to transform the graph of g(x)=Inx into the graph of f(x)=ln(-x)-9.

Option 1: Reflect across the y-axis and translate 9 units to the left
Option 2: Reflect across the x-axis and translate 9 units to the left
Option 3: Reflect across the x-axis and translate 9 units downward
Option 4: Reflect across the y-axis and translate 9 units downward

Answer 1

The correct graph transformation is to reflect the graph of ln(x) across the y-axis and translate it 9 units downward to get the graph of f(x) = ln(-x) - 9.

Step-by-step explanation:

To transform the graph of g(x) = ln(x) into the graph of f(x) = ln(-x) - 9, you need to perform two main operations: reflection and translation. Reflecting across the y-axis is essentially taking the function ln(x) and making it ln(-x), which changes the domain of the function to accept negative x-values instead of positive ones. The next step is a translation: to subtract 9 from the function means to shift the entire graph downward by 9 units. Therefore, the correct transformation is Option 4: Reflect across the y-axis and translate 9 units downward.

Remember that the exponential function e^x and its inverse ln(x) can be used interchangeably where ln(e^x) = x and e^(ln x) = x. This property is useful for various computations involving exponential growth or decay.