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Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section $1.2,$ and then applying the appropriate transformations.

$y=\frac{1}{2}(1-\cos x)$

blue graph represents $\mathrm{f}(\mathrm{x}),$ red graph represents $y=\frac{1}{2}-\frac{1}{2} \cos x$

( GRAPH NOT AVAILABLE )

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 3

New Functions from Old Functions

Functions

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Harvey Mudd College

Boston College

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this question asks us to graft the function by hand. We're big given. Why is 1/2 times one minus co sign axe? The first thing we need to do is need to consider what our parent function is gonna be. We can consider our parent function to simply be co sign of acts without any shifts. Now, in order to get this from this, we need to shift that me to shrink the graph by a factor of two vertically, then reflect it with respect to the X axis. And then lastly, shift 1/2 is 1/2 over here, Units upwards. That's a lot going on here. But let's start with the parent function. Okay, Parent Function Co sign of acts. Looks like Bess given amplitude of one. We can just assume that So then all those things were gonna be drink shrinking by a factor of two vertically reflecting with respect to the X axis and shifting 1/2 unit upwards. It's gonna look like that

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