Question

question 8 of 25
describe the transformation of ( f(x)=sin x ) to ( g(x)=sin x - 7 ).
a. ( f(x) ) is shifted 7 units right to ( g(x) ).
b. ( f(x) ) is shifted 7 units up to ( g(x) ).
c. ( f(x) ) is shifted 7 units left to ( g(x) ).
d. ( f(x) ) is shifted 7 units down to ( g(x) ).

Explanation:

For a function transformation of the form \(g(x) = f(x) + k\), \(k\) determines vertical shift: \(k>0\) shifts up, \(k<0\) shifts down. Here, \(g(x) = \sin x - 7 = f(x) - 7\), so \(k=-7\), meaning a 7-unit downward shift.

Answer:

D. \(f(x)\) is shifted 7 units down to \(g(x)\)