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Sketch the graph of each function.$$f(x)=(x-3)+2$$
Algebra
Chapter 8
More on Functions and Graphs
Section 3
Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions
Graphs and Statistics
Equations and Inequalities
Functions
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to grab this function f of X equals X minus three plus two. This is a transformation off the parent function after blacks equals X. So this indicates that we would be shifting that line three to the right and this indicates that we would be shifting up to now. We could rewrite this. This doesn't work with everything, but was linear ashes like this? It will. We can simplify this. We could combine light terms X minus three plus two to get thanks minus one. And, um, you'll end up with the same thing. So I'm going to do an X Y chart for this simplified function and for the original so that you can see that it gives us the same values. So for f of X equals X minus one, I'm going to choose my ex values and negative too negative. 101 and two And just pluck those in for axe. Someone access negative. To not get a two minus one is negative. Three. When X is negative one, we get highest negative too. When x zero, Why is negative one and so on? And if we were to make an exploit chart using this function. I'm going to go ahead and use the same. Why values? So we start here with X equals Negative too Negative. Two minus three is negative. Side plus two is negative. Three when xnegative one negative one minus three is negative for plus two negative to. So see, this works out to be the same thing. So then to graph the function, just plot these points that we generated. Negative too negative. Three negative one negative too. Zero negative. One 10 and 21 And draw you like those points and continue them on in both precious e. There you have your function.
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