question 10 (1 point) (09.03 mc) in what direction and by how many units is the graph of f(x) = -7 sin(3x +…

question 10 (1 point) (09.03 mc) in what direction and by how many units is the graph of f(x) = -7 sin(3x + π) - 2 vertically and horizontally shifted? a down 2, right π/3 b down 2, left π/3 c up 2, right π/3 d up 2, left π/3

question 10 (1 point) (09.03 mc) in what direction and by how many units is the graph of f(x) = -7 sin(3x + π) - 2 vertically and horizontally shifted? a down 2, right π/3 b down 2, left π/3 c up 2, right π/3 d up 2, left π/3

Answer

Explanation:

Step1: Analyze vertical shift

For a function of the form $y = A\sin(Bx - C)+D$, the vertical - shift is given by $D$. In the function $f(x)=-7\sin(3x + \pi)-2$, $D=-2$. A negative value of $D$ means a downward shift of 2 units.

Step2: Analyze horizontal shift

For the function $y = A\sin(Bx - C)+D$, the horizontal shift is given by $\frac{C}{B}$. First, rewrite $f(x)=-7\sin(3x+\pi)-2$ as $f(x)=-7\sin\left(3\left(x+\frac{\pi}{3}\right)\right)-2$. Here, $B = 3$ and $C=-\pi$. The horizontal - shift is $\frac{-\pi}{3}$, which means a left - shift of $\frac{\pi}{3}$ units.

Answer:

B. Down 2, left $\frac{\pi}{3}$