Question

part 6 of 6
my score: 5.7/21 pts (27.14%)
determine the amplitude, range, period, and phase shift and then sketch the graph of the function using the quarter points.
$y = - \sin(4x - \pi)$
quarter points of $y=\sin x$
$(0,0)$
$\left(\frac{\pi}{2},1\
ight)$
$(\pi,0)$
$\left(\frac{3\pi}{2},-1\
ight)$
$(2\pi,0)$
quarter points of $y = - \sin(4x - \pi)$
$\left(\frac{\pi}{4},0\
ight)$
$\left(\frac{3\pi}{8},-1\
ight)$
$\left(\frac{\pi}{2},0\
ight)$
$\left(\frac{5\pi}{8},1\
ight)$
$\left(\frac{3\pi}{4},0\
ight)$
(simplify your answers. type ordered pairs. type exact answers, using $\pi$ as needed. use integers or fractions for any numbers in the expressions.)
choose the correct graph of $y = - \sin(4x - \pi)$ below.
a.
b.
c.
d.

Explanation:

Step1: Find amplitude

For $y = A\sin(Bx - C)$, amplitude is $|A|$. Here $A=-1$, so amplitude is $|{-1}| = 1$.

Step2: Find period

Period formula: $\frac{2\pi}{|B|}$. $B=4$, so period is $\frac{2\pi}{4} = \frac{\pi}{2}$.

Step3: Find phase shift

Phase shift formula: $\frac{C}{B}$. $C=\pi$, so phase shift is $\frac{\pi}{4}$.

Step4: Analyze range

Since amplitude is 1, range is $[-1, 1]$.

Step5: Match to graph

The function has a short period $\frac{\pi}{2}$ (frequent oscillations) and is reflected over x-axis. The quarter points confirm the shape matches option A.

Answer:

• Amplitude: $1$
• Range: $[-1, 1]$
• Period: $\frac{\pi}{2}$
• Phase shift: $\frac{\pi}{4}$ (to the right)
• Correct graph: A. (the graph with frequent oscillations between $y=-1$ and $y=1$, spanning $x$ from $-\pi$ to $\pi$)