Fill in the blank(s) to correctly complete each sentence.

Question

The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x ________ unit(s) __________ (up/down).

Accepted Answer

Welcome back. Everyone. In this problem, we want to know which of the following statements correctly describes the procedure for obtaining the graph of Y equals 10 plus 12 sin X from the graph of Y equals 12 sin X. For our answer choices. A says that we're going to stretch our graph vertically by a factor of 12 and translate it by 10 units upward. B says we're going to reflect our graph across the X axis and translate it by 10 units upward. C says we're going to translate the graph by 10 units to the right. And B says we're going to translate the graph by 10 units upward. Now, what are we trying to figure out here? Well, we want to know what we need to do to get our new graph from our original graph of Y equals 12 plus sic. So if we picture our original graph here, OK, Y equals 12 sine X which would probably look something like this. Then we are saying, what are we going to do? OK. To get the graph of Y equals 10 plus 12 sine X. When we compare both of those equations, notice that the difference is one is 10 more than the other or new graph is 10 more units than the other. So what does that 10 mean? That's essentially what we're asking now, what do we already know? Will recall that any graph that is written in the form Y equals F of X A function plus C some constant. In this case, 10, it's a vertical translation of the graph of Y equals F of X And the translation is upward by C units if C is positive and downward by C units, if C is negative. So by comparison here, OK, by comparison, and let me make my note that our function here is a vertical. It's right out here is a vertical translation. By comparison, our original graph is Y equals 12 sine X. And our new graph put at in red is equal to 12 sine X plus 10. OK? 10 plus 12 sex. And we can rearrange it to say 12 cyx plus 10. So now notice that the difference here is 10. So our constant C equals 10. So since our constant is 10 and 10 is greater than zero, that means we're going to move it upward by 10 units. In other words, the graph of Y equals 10 plus 12 Sinex would probably look something like this. OK. So that is our new graph. That means then when we look back on our answer choices, the correct answer choice would be answer choice D Thanks for watching everyone. I hope this video helped.

Fill in the blank(s) to correctly complete each sentence.
The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x unit(s) __ (up/down).

Key Concepts

Vertical Shifts in Graphs

Amplitude of a Sine Function

Understanding Sine Function Behavior

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