- consider thefollowing piecewise function and us say f(t) is equal to and they tell united state what it's same to based upon what t is, so if t is much less than or equal to -10, we use this case. If t is between -10 and -2, we use this case. And also if t is better than or same to -2, we usage this case. And then lock ask us what is the worth of f(-10)? so t is going come be same to -10, therefore which situation do us use? for this reason let's see. If t is less than or same to -10, we usage this height case, best over here and also t is equal to -10, that's the one thatwe're trying come evaluate. So we wanna use this case right over here. Therefore f(-10) is going come be equal to -10, everywhere we check out a t here, we substitute it v a -10. - 10 squared minus 5 times, actually I don't have a denominator there, i don't recognize why I wrote it for this reason high. So it's gonna be -10squared minus 5 times -10. For this reason let's see. - 10 squared, that's positive 100 and also then negative, or individually 5 times -10, this is going come be individually -50 or you're going to include 50, therefore this is going to be same to 150. F(10) is 150, 'cause we used this instance up here, 'cause t is -10. Let's do another one of this examples. So, below we have think about the followingpiecewise function, alright. What is the worth of h(-3)? See when h is -3, which case do we use? We usage this case if our xis between negative infinity and zero. And -3 is in betweennegative infinity and zero, therefore we're gonna usage thiscase right over here. If it was hopeful three, us would usage this case. If it was confident 30, us would use this case. Therefore we're going to usage the an initial case again and also so for h(-3), we're gonna take it -3 to the 3rd power. Therefore let's see. H(-3) is going to it is in -3 to the third power i beg your pardon is -27. And also we're done. That's h(-3). Since we're making use of this case, you could practically ignorethese second two instances right over here. Let's do one much more example. This one's a tiny bit different. Below is a graph that the step function g(x) for this reason we deserve to see g(x) best over here. It starts once x equals -9, it's in ~ 3, and then it jumps up, and also then it jumps down. Match each expression v its value. Therefore g(-3.0001), therefore -3.0001, so that's appropriate over here and also g the that, we view is same to 3. Therefore this is going come beequal to 3 ideal over here. G(3.99999) 3.99999, virtually 4, so let's attract a dotted line best here, it's gonna be virtually 4, well g(3.99999) is walk to it is in 7. We view that appropriate over there. So that is equal to 7. G(4.00001). So g(4) is tho 7, yet as soon as we go above 4, us drop down over here, for this reason g(4.00001) is going to be -3. Ns wanna, actually, let's focuson that a tiny bit more. Just how did I know that? fine I know that g(4) is 7 and not -3 due to the fact that we have this dotis circled in increase here and also it's hollow under here. However as quickly as we getany amount bigger than 4, climate the duty drops down to this. Therefore 4.0000, together many, simply slightly over 4, the value of ours functionis walk to be -3. Now let's perform g(9). For this reason g(9), that's once x is 9 and also we go under here. You might be tempted to say it's -3, but you see, at thispoint appropriate over here, we have actually an open circle.


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So that way that when it's not, friend can't say the thefunction is -3 ideal over there and also there's no other placewhere we have a filled-in circle because that x amounts to 9 so the function g actuallyisn't defined at x equates to 9. Therefore I'm gonna put undefinedright end there.