Question

question 20 (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
page 20 of 36

Explanation:

Step1: Recall function transformation rules

For a function \(y = f(x)+k\), if \(k>0\), the graph of \(y = f(x)\) is shifted \(k\) units up. If \(k < 0\), 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. But according to the rule, it should be a shift of \(k\) units up when \(k>0\) and \(|k|\) units down when \(k<0\). The general form of a vertical shift down is \(y = f(x)-m\) (\(m>0\)).

Answer:

False