WEBVTT
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Find the set of zeros of the function π of π₯ equals one-third times π₯ minus four.
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The zeros of the equation will be the place where π of π₯ is equal to zero.
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We want to know what we need to put in for π₯ so that the output of this function is equal to zero.
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To solve for this, weβll need to get π₯ by itself.
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We need to isolate our π₯ variable.
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First, we need to get rid of this times one-third.
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We can do that by multiplying the right side of the equation by three over one.
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Three over one times one over three equals one.
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But if we multiply the right side of the equation by three over one, we have to multiply the left side of the equation by three over one.
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Three over one times zero equals zero.
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Now on the right, we bring down our π₯ minus four.
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One times π₯ minus four equals π₯ minus four.
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Bring down the zero.
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Now we add four to the right side of the equation.
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If we add four to the right, we must add four to the left.
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π₯ minus four plus four equals π₯.
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Minus four plus four cancels out.
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Zero plus four equals four.
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Now we have four equals π₯, or the more common way we write it, π₯ equals four.
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What this means is if we take the value four and plug it in for π₯, four minus four equals zero; one-third times zero equal zero.
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When π₯ equals four, π of π₯ equals zero.
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And thatβs the only place that would create a zero.
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The set of zeros for this function contains only one value: four.