in-3-6-find-the-coordinates-of-the-ordered-pair-with-the-smallest-value-of-y-for-each-function-gx5-x

Question

In $3-6,$ find the coordinates of the ordered pair with the smallest value of $y$ for each function.
$$
g(x)=|5-x|
$$

Finian Lickona · Accepted Answer

All right, So in this exercise, we want to find the coordinates of wth e ordered pair that make the smallest value of why, for the function G of X equals the absolute value of five minus X. So what this really means is why equals the absolute value of five minus X, and the smallest y value that we can have for an absolute value function is always going to be zero, because an absolute value function can never take on a negative value. And so now we need to find the ex Corn. And that makes this why value equal to zero. And so that is obviously going to be five, because five minus 50 So the coordinates that satisfy this equation are five for X and zero for why? So if we plug those in, we get zero equals the absolute value of five minus five. Oh, oops, equals zero. And so it checks out

Mary Brese · Answer

if we graft y equals absolute value of X when x zero wise gonna be zero. We know that this is our V shaped graph. It is the parent function of all family of functions for absolute value grafts. Therefore, it starts at the origin 00 and it is a positive V shape graph with a soap one. So we know we&#x27;re gonna go this direction. And then again Ah, there we go. So this is our absolute value of ex function, and you can see that it&#x27;s lowest point is at the origin. So the lowest why value is equal to zero. However, um, X is from negative. Infinity too. A positive infinity.

Mary Brese · Answer

if I were to graph y equals the absolute value of X over two, minus seven. Using the concept of family of functions, I would want to rewrite this equation and put our fraction of 1/2 on the outside of our absolute value bars because that represents the General Slope. And if I did that, then I would have X here cause 1/2 X equals X. But the question is, is what number would be to the right of the minus sign. So that seven ends up here and that means I would have to put 14 here because 1/2 of 14 is equal to seven. So now I&#x27;ve got my graph that says this shifts to the right 14 and we have a slope of 1/2 and it&#x27;s a positive, absolute value. So if the court will I would have to scale this by twos. Um, if my origin is supposed to be a 00 and we have a shift to the right 2468 10 12 14. That means my Vertex is here now, and we have a slope of 1/2. So 1/2 would look like this to the left, and it&#x27;s gonna go through here, here, here, here to the right. And I can see by graphing this using family of functions that my lowest y value is still, um when Why is equal to zero and again we&#x27;ve got negative. Infinity is less than X, which is less than positive. We can use all riel values of X.

Finian Lickona · Answer

All right. So for this exercise, we need to find the coordinates of the ordered pair that make this equation. Why equals the absolute value of two X plus eight, as small as it can be. So now, for any absolute value function, the smallest value it can take on a zero. Because if you tried to take on a negative value, the absolute value function is just going to convert that to a positive value. So what we really are trying to do is find the ex Cornet that satisfies this particular equation. So I&#x27;m just gonna do some basic algebra or going to subtract eight from both sides. And we have two x equals negative eight. We divide both sides by two, and we get that X equals negative four. So that means that if I plug in X equals negative for into this equation, I get a Y output of zero. And this is actually the smallest value that zero could take on. If I were to plug in a negative five, I&#x27;d have two times negative five, which is 10 plus eight is 18 actually, negative. 10 plus eight is going to come out the negative too. But then the absolute value bars make that a positive too. So, really, the coordinates of the ordered pair that make that function as small as possible are negative for for X and zero for what?

Mrinal Rana · Answer

so finding ordered pairs I have fixed. That&#x27;s the values for which I&#x27;m gonna fight because I&#x27;m gonna find it. The corresponding y values sitting with X equals zero. So for X equals zero, I&#x27;m gonna have why he called three times 0 96 and therefore my equals minus six. The second case, X equals one. I&#x27;m gonna have three times 196 And therefore, why equals negative three. Finally, for X equals two, I&#x27;m gonna have three times to money. Six. Why equals and therefore life. Observe. So therefore, three ordered pairs are gonna be zero minus six one minus three and a 20 So these are my three ordered pairs. Were they given function?

Heather Zimmers · Answer

we have the equation of the line and let&#x27;s find the numbers that are missing in each coordinate pair. So if X equals two, we have, why equals negative three times two plus six. So why equals negative six plus six? So Y equals zero. So this would be the 00.20 And for the other one if y equals negative three, we have negative. Three equals negative three x plus six. We can subtract six from both sides and we get negative. Nine equals negative three x and divide both sides by negative three and we get three equals X So this is the 30.3 negative three.

Problem

In $7-10,$ the domain of each function is the set…

Problem 6 Easy Difficulty

In $3-6,$ find the coordinates of the ordered pair with the smallest value of $y$ for each function.
$$
g(x)=|5-x|
$$

Answer

$(5,0)$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Anna Marie V.

Caleb E.

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Absolute Value - Example 1

Absolute Value - Example 2

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$(5,0)$

Algebra 2 and Trigonometry

Anna Marie V.

Caleb E.

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Caleb E.

Maria G.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry