Question

page 3 of 36 question 3 (mandatory) (1 point) the graph of the function ( g(x)=f(x)+k ) is a shift of ( k ) units down of the graph of ( f(x) ). true false

Explanation:

Step1: Recall function transformation rules

For a function \(y = f(x)+k\), when \(k>0\), the graph of \(y = f(x)\) is shifted \(k\) units up. When \(k < 0\), the graph of \(y=f(x)\) is shifted \(|k|\) units down. The statement says \(g(x)=f(x)+k\) is a shift of \(k\) units down for any \(k\), which is incorrect. It should be a shift of \(|k|\) units down when \(k<0\) and \(|k|\) units up when \(k > 0\).

Answer:

False