Question

What is the range of the function y=1 +2sin(x - 11 )?

Answer 1

Answer:

range of the given function in Interval notation is [-1, 3]

Step-by-step explanation:

i) given function is y = 1 + 2sin(x - 11)

ii) maximum of sin function is 1

iii) therefore maximum of given function $y_{max}$ =  1 + (2$\times$ 1) = 3

iv) minimum of sin function is -1

v) therefore maximum of given function $y_{max}$ =  1 + (2$\times$ -1) = -1

vi) therefore the range of the given function in Interval notation is [-1,3]

Answer 2

Answer:

D. -1 to 3

Step-by-step explanation:

We have been given a function $y=1+2sin(x-11 )$. We are asked to find the range of the function.

We know that since oscillates between $-1$ and 1, that is minimum value of sin is $-1$ and maximum is 1.    

The range of basic sin function is $-1\leq \text{sin}(x-11)\leq 1$.

Now we will multiply all sides by 2.

$-1\cdot 2\leq 2\cdot \text{sin}(x-11)\leq 1\cdot 2$

$-2\leq 2\text{sin}(x-11)\leq 2$

Now we will add 1 on all sides as:

$-2+1\leq 2\text{sin}(x-11)+1\leq 2+1$

$-1\leq 2\text{sin}(x-11)+1\leq 3$

$-1\leq f(x) \leq 3$

Therefore, the range of the given function is $[-1,3]$ and option D is the correct choice.