8. consider the function f(x) = 3 sin(2x). what is the period of the function? (lesson 18.1) (0.5 point) a…

Explanation:

Step1: Recall period formula for $y = A\sin(Bx)$

The period of $y = A\sin(Bx)$ is $T=\frac{2\pi}{|B|}$. For $f(x)=3\sin(2x)$, $B = 2$.

Step2: Calculate the period

$T=\frac{2\pi}{|2|}=\pi$.

Answer:

B. $\pi$

Explanation:

Step1: Analyze vertical - stretch/compression for $y = A\cos(Bx)$

For the function $y = A\cos(Bx)$, the coefficient $A$ determines vertical stretch or compression. For $f(x)=2\cos(\frac{1}{6}x)$, $A = 2$. When $|A|> 1$, the graph of the parent - function $y=\cos(x)$ is vertically stretched by a factor of $|A|$. Here, $A = 2$, so the graph of the parent function is vertically stretched by a factor of 2.

Answer:

D. The graph of the parent function will be vertically stretched by a factor of 2

Explanation:

Step1: Identify period from the graph

The period is the horizontal distance between two consecutive identical points on the graph. Looking at the graph, we can see that the distance between two consecutive peaks (or troughs) is $\pi$.

Answer:

A. $\pi$

Explanation:

Step1: Recall amplitude definition

The amplitude of a trigonometric function is half the vertical distance between the maximum and minimum values of the function. From the graph, the maximum value is 4 and the minimum value is - 4. The vertical distance between them is $4-(-4)=8$, and the amplitude is $\frac{8}{2}=4$.

Answer:

B. 4