Question

standard 15 homework
score: 9/21 answered: 9/20
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question 15
write the equation of a graph that is obtained by vertically stretching the graph of ( y=sin (x) ) by a factor
of 6 and shifting it 9 units to the right and 3 units down.
( f(x)= )

Explanation:

Step1: Vertical stretch

For a function \(y = f(x)\), a vertical stretch by a factor \(a\) gives \(y=a\cdot f(x)\). Here \(f(x)=\sin(x)\) and \(a = 6\), so we get \(y = 6\sin(x)\).

Step2: Horizontal shift

For a function \(y = f(x)\), a shift \(h\) units to the right gives \(y=f(x - h)\). Here \(h = 9\), so we have \(y=6\sin(x - 9)\).

Step3: Vertical shift

For a function \(y = f(x)\), a shift \(k\) units down gives \(y=f(x)-k\). Here \(k = 3\), so \(y=6\sin(x - 9)-3\).

Answer:

\(6\sin(x - 9)-3\)