Question

Write a rule for g that represents a reflection in the x-axis, followed by a translation 9 units right of the graph of f(x)=log2x

Answer 1

The rule for g that represents a reflection in the x-axis, followed by a translation 9 units right of the graph of f(x)=log2x is g(x) = -log2(-x + 9).

Step-by-step explanation:

The rule for g that represents a reflection in the x-axis, followed by a translation 9 units right of the graph of f(x) = log2x can be written as:

1. First, reflect the graph of f(x) = log2x in the x-axis. This can be achieved by changing the sign of the function, resulting in f(-x) = -log2(-x).
2. Next, translate the reflected graph 9 units to the right. This is done by replacing x with (x - 9) in the expression, giving f(-(x - 9)) = -log2(-(x - 9)).

So, the rule for g(x) is g(x) = -log2(-x + 9).

Answer 2

Step-by-step explanation:

To create a rule for the transformation described, we'll break it down into two steps: reflection in the x-axis and translation 9 units to the right. Let's denote the transformed function as g(x).

Step 1: Reflection in the x-axis

To reflect a function in the x-axis, we need to negate the y-values. Therefore, for any point (x, y) on the graph of f(x), the reflected point will be (x, -y).

Step 2: Translation 9 units to the right

To translate the function 9 units to the right, we need to subtract 9 from the x-values. Therefore, for any point (x, y) on the reflected graph, the translated point will be (x - 9, -y).

Combining both steps, we can express the transformation as follows:

g(x) = -(log2(x - 9))

The function g(x) is obtained by reflecting the graph of f(x) = log2(x) in the x-axis and then translating it 9 units to the right.