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When f(x) becomes f(x) - 1:
This is a vertical shift that moves the function down by 1. Therefore, the y-intercept also moves down by 1. Nothing else is affected because you simply nudged it downwards.
When f(x) becomes -f(x) + 1
Again, the vertical shift here only nudges it. However, it's also multiplied by -1, which reflects the entire function over the x-axis because anything that was positive becomes negative and vice versa. This end behavior changes the same way; if it went up on one side, it'll now go down instead and vice versa.
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So what regions would be increasing/decreasing?
well...Basically for f(x) + 2 the y-intercept moves up two units
For (-1/2)*f(x) the y-intercept flips to negative if it was positive and to positive it was negative.
ok! That makes sense. I'm not getting the end behavior thing though
ok so how about this let me re-explain it for you :) ...
f(x)+2 is a translation +2 in the direction of the y-axis (i.e. upwards)
-1/2f(x), the graph get turned upside down, so times all the y co-ordinates by -1. The y coordinates will also be multiplied by a 1/2. So basically multiply all your y coordinates by a 1/2