Question

use the graph of ( y = f(x) ) to graph the function ( g(x)=-f(x) ).

Explanation:

Step1: Identify the transformation

The function \(g(x)=-f(x)\) is a reflection of \(y = f(x)\) over the \(x\) - axis.

Step2: Reflect each point

For each point \((x,y)\) on \(y = f(x)\), the corresponding point on \(y=-f(x)\) is \((x, -y)\).

• If \(f(x)\) has a point \((x_1,y_1)\), then \(g(x)\) has the point \((x_1,-y_1)\)
• For example, if \(f(x)\) has a peak at \((1,5)\), then \(g(x)\) has a point at \((1, - 5)\)
• If \(f(x)\) has a minimum at \((-2,-5)\), then \(g(x)\) has a point at \((-2,5)\)

Answer:

Graph the function \(y = g(x)\) by reflecting each point of \(y = f(x)\) over the \(x\) - axis.