# Question Video: Completing a Table of Values for a Piecewise Function Mathematics • 10th Grade

Find the missing table values for π(π₯) = 2^π₯ if π₯ < β2, π(π₯) = 3^π₯ if β2 β€ π₯ < 3, and π(π₯) = 2^π₯ if π₯ β₯ 3.

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### Video Transcript

Find the missing table values for the piecewise function π of π₯, which is equal to two to the power of π₯ if π₯ is less than negative two, three to the power of π₯ if π₯ is greater than or equal to negative two and less than three, or two to the power of π₯ if π₯ is greater than or equal to three. And then we have a table with the values of π₯, negative three, zero, and three.

Remember, when we have a function defined by different functions depending on its value of π₯, we call it a piecewise function. And according to our table, weβre looking to find the value of π of π₯ when π₯ is negative three. So thatβs π of negative three. We also want to find π of zero and π of three. And so we need to pay extra careful attention to the part of the function weβre going to use for each value of π₯. Letβs begin with π of negative three. Here, π₯ is equal to negative three. And so, since negative three is less than negative two, we need to use the first part of our function, that is, two to the power of π₯.

And so to find π of negative three, weβre going to substitute π₯ equals negative three into that part of the function. And we get π of negative three is two to the power of negative three. And at this stage, we might recall that a negative power tells us to find the reciprocal. So π to the power of negative π, for instance, is one over π to the power of π. And this means then that two to the power of negative three is one over two cubed, which is equal to one over eight. And so the first value in our table is one-eighth. Letβs repeat this process for π₯ equals zero.

This time zero is between negative two and three, so weβre going to use the second part of our function. And so, π of zero is found by substituting π₯ equals zero into the function π of π₯ equals three to the power of π₯. So thatβs three to the power of zero. Now, of course, at this stage, we might recall that anything to the power of zero is equal to one, so π to the power of zero is simply equal to one. And thatβs the second value in our table. Letβs repeat this process for the third and final column in our table.

The third part of our piecewise function is used when π₯ is greater than or equal to three. So weβre going to use this value when π₯ is equal to three. And this means that π of three is two cubed, which is simply equal to eight. And so we pop eight in the final part of our table. The missing table values for our piecewise function π of π₯ are one-eighth, one, and eight.