In Exercises 1–6, determine the amplitude of each function. Then ...

Question

In Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π.

y = -3 sin x

Accepted Answer

Hello, everyone. We are asked to identify the amplitude of the given function then graphic and its parent function Y equals the sign of X. In the same Cartesian plane, we are going to consider the domain of 0 to 2 pi. For both functions, the function we are going to be graphing is Y equals negative sign of X. So I'm gonna start by graphing my parent function. So Y equals the sign of X. I'm gonna graph that in blue, I recall that when I'm working with, why was the sign of X? My X and Y values should be as follows. So we should start at 00. And then since the period is two pi each X value is pi divided by two spaces apart. So our second X value is pi divided by two, third, X value is pi fourth is three pi divided by two and the fifth would be two pi. And our traditional parent function for a sine wave, the Y values follow a pattern of 010, negative 10. So it starts at 00. It increases to one decreases back to Y equals zero, decreases to negative one and then increases back to zero. So I'm gonna graph this sine wave. So 00 pi divided by two. Is it one pie is back at zero pi divided by or sorry, three pi divided by two. Is that negative one and two pi is at zero? So we have this little narrow sine wave that I just drew in blue on our Cartesian plane. So now that I have our parent function graph, I'm gonna work on our function. So Y equals negative 14 sign of X were asked to find the amplitude. So the amplitude is the absolute value of A A is our value that is directly in front of sign. So it'll be the absolute value of negative 14, which is 14. So this means if you compare it to our parent function, the one and negative one, we just drew will actually increase to 14 and negative 14. Also I noticed that A is negative. So this means that our sine wave will start off decreasing instead of increasing. So let's make an X and Y table for this since the period didn't change the and there's no big shift. Our X values are actually gonna be exactly the same as they were in our parent function. So zero pi divided by two hi three pi divided by two and two pie and zero will still start at the Y value of zero because A is negative, our next value will be negative and our amplitude is 14. So this will be negative 14 for our second Y value. And then I'll go back up to zero and then it'll continue increasing to our amplitude of 14 and decrease again to zero. So I'm gonna put these points on the graph and try to make a OK looking sine wave. So I'm gonna start at 00 and then I decrease to pi divided by two negative 14 and then increase back to 00. Then we're gonna increase to three pi divided by two up to 14 for the Y value and then back down to 0042 pi. So let's see if I can draw this and look somewhat like a sine wave. I know I'm not a perfect artist. All right. So we have covered the space between and including 0 to 2 pi for both functions and they are drawn on the same Cartesian plane. So I think we did what was asked of us, you can tell that they are definitely have some differences. Have a nice day.

In Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = -3 sin x

Key Concepts

Amplitude

Graphing Trigonometric Functions

Period of Sine Function

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