what is the range of the function y = 3sinx?\n○y≥0\n○ - 1≤y≤1\n○y≤3\n○ - 3≤y≤3\n\nquestion 10 1 pts\nwhat is…

what is the range of the function y = 3sinx?\n○y≥0\n○ - 1≤y≤1\n○y≤3\n○ - 3≤y≤3\n\nquestion 10 1 pts\nwhat is the period of the graph of the equation y = 2sin4x?\n○π/2\n○π\n○4π\n○8π\n\nquestion 11 1 pts\nwhich number is not an element of the range of y = sinx?\n○1\n○2\n○ - 1\n○0

what is the range of the function y = 3sinx?\n○y≥0\n○ - 1≤y≤1\n○y≤3\n○ - 3≤y≤3\n\nquestion 10 1 pts\nwhat is the period of the graph of the equation y = 2sin4x?\n○π/2\n○π\n○4π\n○8π\n\nquestion 11 1 pts\nwhich number is not an element of the range of y = sinx?\n○1\n○2\n○ - 1\n○0

Answer

Explanation:

Step1: Recall range of basic sine function

The range of $y = \sin x$ is $- 1\leqslant\sin x\leqslant1$.

Step2: Find range of $y = 3\sin x$

Multiply the inequality by 3: $-3\leqslant3\sin x\leqslant3$. So the range of $y = 3\sin x$ is $-3\leqslant y\leqslant3$.

Step3: Recall period formula for $y = A\sin(Bx)$

The period formula for $y=A\sin(Bx)$ is $T=\frac{2\pi}{|B|}$.

Step4: Calculate period of $y = 2\sin4x$

For $y = 2\sin4x$, $B = 4$. Then $T=\frac{2\pi}{4}=\frac{\pi}{2}$.

Step5: Recall range of $y=\sin x$

The range of $y = \sin x$ is $[-1,1]$. The number 2 is not in the interval $[-1,1]$.

Answer:

Question 1: -3 ≤ y ≤ 3 Question 10: $\frac{\pi}{2}$ Question 11: 2