What is the maximum value of y = -1 + 4 (sin 2x)?

Question

I'm so lost on how to do this.
Please show how you got your answer and not just the answer
Thanks
=]
A. 3
B. 4
C. 5
D. 6
E. 7

Answer 1

Well maximum value of sinA = 1

So maximum value of sin 2x = 1 (Let A = 2x)

So maximum value of 4 sin2x = 4 * 1 = 4

So maximum value of

y = - 1 + 4 sin2x

= -1 + 4 = 3 ← Answer A

Answer 2

You can answer this question easily just by draw its graph.. The y=sin x graph is "S" like graph. it has maximum value of 1.

So, if sin x has one "S" like curve from x=0~x=2pi, so sin 2x has two "S" like curve from x=0~x=2pi. But it has nothing to do in this question actually.

The main point is, if sin x has the maximum point of 1, then 4 (sin x) has maximum point of 4. Then, the -1 means that the whole graph moved down 1 unit.

So, if you draw the graph of y=-1+4(sin 2x), it will be;
a) has two "S" like curve between x=0~x=2pi;
b) has maximum point of 3;
c) has minimum point of -5.

So, for this question, the answer should be (A).

Answer 3

A. 3
For any a, -1<=sin(a)<=1. So, having "2x" is insignificant. Let sin(2x) equal the maximum value of 1.

y = -1 + 4(1) = -1 + 4 = 3

Answer 4

It's easy once you realize that 'sin' only goes between -1 and 1.

The maximum (greatest positive) value of this equation is therefore when sin2x = 1. Put this in the equation and you get:
y = -1 + 4 = 3

So the answer is A.

Answer 5

Think abou t this. WHAT is the maximum value that sine function EVER return for any value of X?

ONE correct?

Then, the fact that the argument to sin is 2x doesn't matter. It will still return maximum of ONE.

Then solve this function: y= -1 + 4(1)

The answer is 3

Answer 6

The amplitude of this graph is 4, and the vertical shift is down one. If there were no vertical shift, the max would be 4, but since the vertical shift is down 1, the max is 3.