Question

use the graph of y = f(x) to graph the function g(x) = f(-x) - 2. choose the correct graph of g below. a. graph a b. graph b c. graph c d. graph d

Explanation:

Step1: Analyze the transformation \(g(x)=f(-x)-2\)

The transformation \(y = f(-x)\) reflects the graph of \(y = f(x)\) about the \(y -\)axis. The transformation \(y=f(-x)-2\) then shifts the graph of \(y = f(-x)\) down by 2 units.

Step2: Check the key - point transformation

Let's assume some key points on \(y = f(x)\). For example, if \((x_0,y_0)\) is on \(y = f(x)\), then on \(y = f(-x)\) the point is \((-x_0,y_0)\), and on \(y = f(-x)-2\) the point is \((-x_0,y_0 - 2)\)

Step3: Visual inspection of the graphs

When we reflect the given graph of \(y = f(x)\) about the \(y -\)axis and then shift it down by 2 units, we compare with the options.
The graph of \(y = f(x)\) has a "zig - zag" shape. Reflecting about the \(y -\)axis changes the \(x -\)coordinates of the points (if a point \((a,b)\) is on \(y = f(x)\), then \((-a,b)\) is on \(y = f(-x)\)) and then shifting down by 2 units changes the \(y -\)coordinates (the new \(y -\)coordinate is \(b - 2\)).

Answer:

C.