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In $3-6,$ find the coordinates of the ordered pair with the smallest value of $y$ for each function.$$f(x)=\left|\frac{x}{2}-7\right|$$

$(14,0)$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 4

Absolute Value Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

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Lectures

01:32

In mathematics, the absolu…

01:11

01:09

In $3-6,$ find the coordin…

01:03

01:26

Find three ordered pairs t…

01:33

For $f(x)=-x^{2}+6 x-7,$ t…

04:00

Find the maximum and the m…

00:43

Complete the given ordered…

02:41

Find the absolute maximum …

01:58

Determine which of the ord…

00:40

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've got my graph that says this shifts to the right 14 and we have a slope of 1/2 and it'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'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've got negative. Infinity is less than X, which is less than positive. We can use all riel values of X.

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