Question

homework: section 7.2a more on the graphs of sine and cosine obj 1 - 2
part 6 of 6
my score: 7.7/21 pts (36.67%)
determine the amplitude, range, period, and phase shift and then sketch the graph of the function using the quarter points.
$y = -4\cos(2x - \pi)$
quarter points of $y=\cos x$
$(0,1)$ $left(\frac{\pi}{2},0\
ight)$ $(pi,-1)$ $left(\frac{3\pi}{2},0\
ight)$ $(2\pi,1)$
quarter points of $y = -4\cos(2x - \pi)$
$left(\frac{\pi}{2},-4\
ight)$ $left(\frac{3\pi}{4},0\
ight)$ $(pi,4)$ $left(\frac{5\pi}{4},0\
ight)$ $left(\frac{3\pi}{2},-4\
ight)$
(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 $y = -4\cos(2x - \pi)$ below.
○ a.
○ b.
○ c.
○ d.
7.2.19-step by step
question | 1/1 pt
7.2.20-step by step
question | 0/1 pt
7.2.22-step by step
question | 0/1 pt
7.2.24-step by step
question | 0/1 pt
7.2.14a
question | 0/1 pt

Explanation:

Step1: Find amplitude

Amplitude = $|A|$ for $y=A\cos(Bx-C)$.
Here $A=-4$, so amplitude = $|-4| = 4$.

Step2: Calculate period

Period = $\frac{2\pi}{|B|}$.
Here $B=2$, so period = $\frac{2\pi}{2} = \pi$.

Step3: Compute phase shift

Phase shift = $\frac{C}{B}$.
Here $C=\pi$, $B=2$, so phase shift = $\frac{\pi}{2}$.

Step4: Identify range

Range is $[-|A|, |A|] = [-4, 4]$.

Step5: Match to correct graph

The function has amplitude 4, period $\pi$, phase shift $\frac{\pi}{2}$ right, and reflects over x-axis (due to negative A). This matches graph A.

Answer:

Key Values:

• Amplitude: $4$
• Period: $\pi$
• Phase Shift: $\frac{\pi}{2}$ (right)
• Range: $[-4, 4]$

Correct Graph:

A. (the graph with y-range -5 to 5, period $\pi$, shifted right $\frac{\pi}{2}$, and reflecting $y=4\cos(2x)$ over the x-axis)