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

8. consider the function f(x) = 3 sin(2x). what is the period of the function? (lesson 18.1) (0.5 point) a 1/2π b π c 2π d 4π 9. consider the function f(x) = 2 cos(1/6x). which of the following statements is true? (lesson 18.1) (0.5 point) a the graph of the parent function will be vertically compressed by a factor of 1/2 b the graph of the parent function will be vertically compressed by a factor of 1/6 c the graph of the parent function will be vertically stretched by a factor of 2 d the graph of the parent function will be vertically stretched by a factor of 6

8. consider the function f(x) = 3 sin(2x). what is the period of the function? (lesson 18.1) (0.5 point) a 1/2π b π c 2π d 4π 9. consider the function f(x) = 2 cos(1/6x). which of the following statements is true? (lesson 18.1) (0.5 point) a the graph of the parent function will be vertically compressed by a factor of 1/2 b the graph of the parent function will be vertically compressed by a factor of 1/6 c the graph of the parent function will be vertically stretched by a factor of 2 d the graph of the parent function will be vertically stretched by a factor of 6

Answer

Explanation:

Step1: Recall period - formula for sine function

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

Step2: Calculate the period

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

Step3: Recall vertical - stretch/compression rule for cosine function

For the function $y = A\cos(Bx)$, the amplitude is $|A|$. If $|A|> 1$, the graph of the parent - function $y=\cos(x)$ is vertically stretched by a factor of $|A|$, and if $0<|A|<1$, the graph is vertically compressed by a factor of $|A|$. For the function $f(x)=2\cos(\frac{1}{6}x)$, $A = 2$.

Answer:

  1. B $\pi$
  2. D The graph of the parent function will be vertically stretched by a factor of 2