Determine if each equation is a function. y = 2 x + 3 y=2x+3

Are asked in this problem to determine if each equation is a function, and here we're given the equation y is equal to two x plus three. So we know that this is a relation that we're dealing with, but is it a function? Well, what we're going to do is test some x values here. Because remember, every x value or input that you have has to result in at most one y value or output in order for it to be a function. Now what I'm first going to do is try an x value of zero. So we'll have two times zero plus three, which all just comes out to three. Now notice I have one input, which is zero, and I get one output, which is three. So we're good. Let's try another x value, let's try one this time. So we have an x value of one, and two times one plus three comes out to five. Notice that our one input gives us one output of five, so we're still good. Let's try a negative number. Let's try, say, negative two. I'm just choosing a random x value here, plus three. Well, two times negative two is four, plus three would give us negative one. Notice that one x value, negative two, gave us one y value of negative one. So notice that really, no matter what we try, we only ever seem to be getting one output or one y value. And you can try a whole bunch of different inputs for x. You're gonna find every time it's just gonna give you one y value. You could also recognize that this is in fact a linear equation. This would be a line on a graph, which we know would pass the vertical line test. So no matter how about you or no matter how you go about this, you're going to find every single time this does come out to one output, meaning it is in fact a function. Hope you found this helpful.

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30m

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16m

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9m

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17m

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40m

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41m

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30m

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59m

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24m

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6m

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21m

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33m

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34m

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41m

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25m

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19m

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57m

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24m

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27m

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47m

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10. Relations and Functions

Introduction to Relations and Functions

Beginning & Intermediate Algebra

10. Relations and Functions

Introduction to Relations and Functions

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Determine if each equation is a function.
$y = 2 x + 3$

Function

Not a function

Cannot be determined

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Recall the definition of a function: a relation where each input (x-value) corresponds to exactly one output (y-value).

Look at the given equation: $y = 2x + 3$. This is a linear equation where y is expressed explicitly in terms of x.

For every value of x, you can calculate exactly one value of y by substituting x into the equation.

Since each x produces only one y, the equation passes the vertical line test (if graphed, no vertical line would intersect the graph at more than one point).

Therefore, based on the definition and the form of the equation, conclude that this equation represents a function.