Question

the function f(x) is shown in the graph.
if g(x) = f(x - 2), determine the x-intercept of g(x).

Explanation:

Step1: Find the x - intercept of \(f(x)\)

From the graph of \(f(x)\), when \(y = f(x)=0\), \(x = 2\). So the x - intercept of \(f(x)\) is \(x = 2\).

Step2: Analyze the transformation \(g(x)=f(x - 2)\)

The transformation \(y = f(x)\) to \(y = f(x - h)\) is a horizontal shift. For \(g(x)=f(x - 2)\), it is a shift of \(f(x)\) to the right by 2 units.
Let the x - intercept of \(f(x)\) be \(x_1\) and of \(g(x)\) be \(x_2\). Using the transformation rule \(x_2=x_1 + 2\).

Answer:

The x - intercept of \(g(x)\) is \(x=4\)