For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1)...

Question

For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).

$f (x) = {\begin{matrix} 2 + x & if x < - 4 \\ - x & if - 4 \leq x \leq 2 \\ 3 x & if x > 2 \end{matrix}$

Accepted Answer

Welcome back. I am so glad you're here. We are given this piecewise function and were asked to evaluate four values for X for it. Well, let's break this piecewise function down a little bit. So we've got a five X and three different situations, three different pieces. And I'm actually going to draw these out on a number line just to visualize them a little bit differently. One of these says that if X is less than negative five, okay, we'll put a zero on here. And so we're talking about X being less than negative five, not including negative five. So that's here and toward negative infinity. If X is that value less than negative five, then what we are going to do is plug the X into X plus five and that will be how we sell for X. Now, if X is going to be between and including negative five and three, okay. So we've got from negative five. Now let's label three on the number line. If it is from those including negative to 3, then the way that we solve for X is it's going to be a negative four, X, we plug X into negative four X and then evaluate and then the last one here is if X is greater than three, so that's not including three, but all the way up to positive infinity. If X falls into that range, then we are going to plug it into X divided by five, plug it in there and then evaluate. So what are our four X values? We have F of negative six. Okay. Where does negative six fall? Well, that is less than negative five. So we're going to plug in F of negative six in here. How about this next one? F of negative four? While negative four is between negative five and three. So we're going to evaluate F of negative four in here. How about half of one? Well, one is also between negative five and three. So we're going to evaluate F of one in the same space as F of negative four. And how about F of positive for well positive for is greater than three. So we're going to plug off of four in to this last one. Now we can just plug these values in for X and solve. So for F of negative six, we're plugging in negative six plus five and negative six plus five equals negative one. So for F of negative six, that's equal to negative one. Now let's plug in for negative four, we have negative four, not times acts but times negative four, negative four times negative four is a positive 16. So F of negative four equals 16. Now, for F of one, we are plugging one end negative four times not X but one negative four times one is negative four. So F of one equals negative four. And lastly for F of four, we're plugging that in for X 4/5 instead of X over five that doesn't simplify anymore. So we get 4/5 for F of four. Alright. We've got our four answers for F of negative six equals negative one, F of negative four equals 16 F of one equals negative four and F of four equals 4/5. Now which answer choice matches that and that is going to be answer choice a well done. We'll catch you on the next one.

For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).
$f (x) = {\begin{matrix} 2 + x & if x < - 4 \\ - x & if - 4 \leq x \leq 2 \\ 3 x & if x > 2 \end{matrix}$

Key Concepts

Piecewise-Defined Functions

Evaluating Functions at Specific Points

Inequalities and Interval Notation

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