Question

Pre-Cal help

Answer 1

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.

Answer 2

@Raindropssss

Answer 3

@kim21 yes

Answer 4

So what regions would be increasing/decreasing?

Answer 5

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.

Answer 6

ok! That makes sense. I'm not getting the end behavior thing though

Answer 7

ok so how about this let me re-explain it for you :) ...

Answer 8

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

Answer 9

Thanks!!

Answer 10

welcome :)