Question

complete the sentence below. suppose that the graph of a function f is known. then the graph of y = f(x - 2) may be obtained by a — shift of the graph of f — a distance of 2 units. suppose that the graph of a function f is known. then the graph of y = f(x - 2) may be obtained by a horizontal shift of the graph of f a distance of 2 units.

Explanation:

Step1: Recall function transformation rules

For a function \(y = f(x)\), if we have \(y=f(x - h)\), it is a horizontal shift. When \(h>0\), the graph shifts to the right by \(h\) units.

Step2: Apply the rule to \(y = f(x - 2)\)

Here \(h = 2\). According to the rule \(y=f(x - h)\) (horizontal - shift rule), the graph of \(y = f(x-2)\) is obtained by a horizontal shift of the graph of \(y = f(x)\). Since \(h=2>0\), the shift is to the right by 2 units.

Answer:

horizontal; to the right