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Problem 42 Hard Difficulty

Evaluate $f(-3), f(0),$ and $f(2)$ for the piecewise defined function. Then sketch the graph of the function.
f(x)=\left\{\begin{array}{ll}{3-\frac{1}{2} x} & {\text { if } x<2} \\ {2 x-5} & {\text { if } x \geq 2}\end{array}\right.




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Video Transcript

were given. Function affects NFL. Brett's constant has come from composed of two different functions. Ocean A and B Will potions are linear. However, these functions exist. But in a certain domain where potion a exists wherever excess lesson to in function be Is this where were access greater than or equal to two? So for this problem, you're told to graph for these three specific acquaints in order to do that first, very going to draw a graph. So now we're going to draft our little while Are functions that compose the create that little X that make, um so we have Why is it so for function a air two x blustery wherever excess lesson to. So in order to graft us now we need we need a few points. So since cycles listen to let's start with zero, which will give us the y intercept. So negatives have I'm zero must drink it straight. That's just give us there. What? Interested? Okay, we have want me down. No, we can use many other points, however, so it's excess lesson to we should looking to. Uh But then that point will have a hole in it. Since X ISS less than two. This motion does not exist when excess, too. It doesn't have any value or has undefined value or wherever access to. So let's go to value prices, too. We're gonna get one over two. Really? Good. You come on. Okay. However, this is a home looking mentions is the function is wherever eggs this western too. So we congrats. That too. 10 23 Our Ryan just up and re we'll draw the flying unless there first. That's a That's the graph for first function. Not really graft. The second motion would just be Toby is I s secrets to X minus five wherever X is greater than or equal to. So we also need to points for this function. So let's start with two since two. It's the least, um, who is the smallest number. So why to to And then that is going to be equal to negative one. So for two, we have to commit negative one, and then we can plug in three. So, uh, so to Tim story minus five six minus 51 So that's gonna give us they re coming one in here. There won't be a whole but it'll be filled, says X. Does the function does exist whenever access to that motion? It's the domain is too. So this is filled. So let's draft these planes Supermen, native, one build and three comma. What is also filled? Then we can graph it and thats Listen, this is our