I can't seem to understand the logic behind these functions. Since H(x) is a constant, I feel like it would not change at all for the transformations in part a, c, and d, since it is perfectly horizontal.
First, in (a) if we shift this function by 10 units to the right, we only change the domain right? That is, we change only from where y=1 begins (X≥10 now).
In (b) do we shift right by 1/2? Shouldn't we be shifting left by 1 cuz of the +1? Also, since the graph is merely two constants, we can't again shift it horizontally, so we'll be changing the domain again as in (a)?
C is all clear.
For (d), I've heard the solution is a square wave? When you see something like H(x) = 1 transformed to H(sin(x)), what do you do algebraically? Do you input any function into another or something? If you can, please show this on a page; but an explanation here would also do just fine. Alternatively, you can also redirect me to a video or page where all this is explained.
First, in (a) if we shift this function by 10 units to the right, we only change the domain right? That is, we change only from where y=1 begins (X≥10 now).
In (b) do we shift right by 1/2? Shouldn't we be shifting left by 1 cuz of the +1? Also, since the graph is merely two constants, we can't again shift it horizontally, so we'll be changing the domain again as in (a)?
C is all clear.
For (d), I've heard the solution is a square wave? When you see something like H(x) = 1 transformed to H(sin(x)), what do you do algebraically? Do you input any function into another or something? If you can, please show this on a page; but an explanation here would also do just fine. Alternatively, you can also redirect me to a video or page where all this is explained.