Select the graph of y = 3 sin (x - 1).

D.

Step-by-step explanation:

We can cancel out choice A and choice B because both graphs' amplitude are 2. (Amplitude determines the max-min so if amplitude is 2 then max is 2 and min is -2)

Now for graph C and D, if we do not know how does sine graph shift, we will do substitution to find value of y when x = a.

Let's try x = 0 because both graphs have different y-value for x = 0.

Let's recall the negative measure;-

Therefore:-

We know that π/4 is equivalent to 45° because π is defined as 180° and 180°/4 is 45°

Using hand method, sin(45°) is √2/2

Looks like when we substitute x = 0, the y-value becomes negative.

The only graph that's reasonable is D.

Another method is you substitute x = π/4 in which would make y-value = 0.

Since π/4 is between 0 < x < π/2, the graph D is correct because graph C may have amplitude of 3 but y-value does not become 0 when substitute x = π/4

So D.

a

step-by-step explanation: