Question

use graph of ( y = f(x) ) to graph ( g(x)=f(-x) ) the points of ( y = f(x) ) are ( (-2,4)(0,4)(2,4) )

Explanation:

Step1: Understand the transformation

The transformation \(g(x) = f(-x)\) reflects the graph of \(y = f(x)\) over the \(y\) - axis. For a point \((x,y)\) on \(y = f(x)\), the corresponding point on \(y = g(x)\) is \((-x,y)\).

Step2: Apply the transformation to each point

• For the point \((- 2,4)\) on \(y = f(x)\):

Substitute \(x=-2\) into \(g(x)=f(-x)\). Let \(x_1=-2\), then \(g(x_1)=f(-(-2)) = f(2)\). The \(y\) - value remains \(4\), and the new \(x\) - value is \(2\). So the corresponding point on \(y = g(x)\) is \((2,4)\).

• For the point \((0,4)\) on \(y = f(x)\):

Substitute \(x = 0\) into \(g(x)=f(-x)\). Since \(-x=-0 = 0\), the point \((0,4)\) on \(y = f(x)\) corresponds to the point \((0,4)\) on \(y = g(x)\) (because \(g(0)=f(-0)=f(0)\)).

• For the point \((2,4)\) on \(y = f(x)\):

Substitute \(x = 2\) into \(g(x)=f(-x)\). Let \(x_2 = 2\), then \(g(x_2)=f(-2)\). The \(y\) - value remains \(4\), and the new \(x\) - value is \(-2\). So the corresponding point on \(y = g(x)\) is \((-2,4)\).

Answer:

The points on \(y = g(x)\) are \((2,4)\), \((0,4)\), \((-2,4)\)