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How do I write this function?

How do I write this function? Topic: How to write absolute value
June 27, 2019 / By Christina
Question: Write a function that represents the data set (-4, 16), (1,1), (3,9), (4, 16), (7, 49). what does this symbol (^) mean? i don't remember learning how to write functions this way, so this is brand new to me
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Best Answers: How do I write this function?

Avelina Avelina | 10 days ago
f(x)=|x^2| edit: it seems a lot of people answered this with f(x)=x^2 but the first coordinate in your set makes the above untrue, as -4^2 = -16. but the |-16| <-- (absolute value) of -16 is 16. so f(x) = |x^2| addresses all of the points in the set, including the first. ^2 = squared. for example f(x)=|x^2| is the absolute value of x squared.
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Avelina Originally Answered: Pre-Calculus Function. Use function notation to write h in terms of the parent function f?
You are given this 'parent' function which is just a term to express a function that you are going to be working with. When I say working with, I mean you're going to change it by moving it. x^3 is a graph you should be able to draw. As I recall, it sort of snakes up through the origin from the lower left quadrant of the Cartesian plane, goes through the origin and then snakes up to through the right Cartesian plane. You should know how to graph it - use a graphing calculator if you feel more comfortable with that - but this is one of the basic graphs you should recognize. Then you are asked to transition up 5. That means that without changing the shape of the graph, you move it up 5 units. Where it crossed the y axis was the origin (0,0). Now it's going to cross the y axis 5 units up at (0,5). Transition right 2. That means that now that you've 'lifted' the graph by moving it up 5, you should move it to the right 2 units. So where you had a point I just mentioned, (0,5), you're going to change that - without changing the shape of the graph at all - so that it is (2,5). The way that you express what you just did to the graph is to change the equation so that it shows this. That is how you end up with h(x)=f(x-2)+5. When you move up, it's plus something. When you move down, it's minus something. When you move to the right, it's -2 after the x and in parentheses and when you move to the left, it's +2 after the x and in parentheses. Without going into a big explanation of why that is that way, that's just the way it gets written. When you have the second h(x)=x^2-6, the only thing you are doing is moving down -6 units. You don't have an x in parentheses. These are translations of the graph. Read more about this in your textbook and you'll see how it's done....
Avelina Originally Answered: Pre-Calculus Function. Use function notation to write h in terms of the parent function f?
These are rules of translation. See this answer for an explanation: http://answers.yahoo.com/question/index;... Basically, when you have f(x) and f(x) + b, the whole graph is shifted up by b because for every value you evaluate f(x) for, you're adding b to it. To shift left and right, you do f(x+a). The graph will be shifted left by a. (the graph moves in the opposite direction if a or b are negative)
Avelina Originally Answered: Pre-Calculus Function. Use function notation to write h in terms of the parent function f?
** If by writing g in terms of f you mean the composite function g(f(x)), then we have: g(f(x)) = g(x^2) = 1/4(x^2 + 4)^2 - 5. ** Let's say that g(f(x)) = h(x) ** Then our new composite function is: ** h(x) = 1/4(x^2 + 4)^2 - 5. ** I hope this helps --Jennifer L.

Avelina Originally Answered: How do you write a function rule?
you have to decided on the rule to get from the input numbers to the output numbers (and it has to be the same for ALL of them). so if our t-chart looks like this: INPUT OUTPUT 1..............3 2..............5 3..............7 4..............9 5.............11 then we put in an input number, multiply it by 2 and add 1 to get the output number (and it works for ALL of the pairs). so if we say that x is the input number then f(x) is the output and our rule would look like this: f(x) = 2x + 1 (the output is 2 times the input plus one) this can be graphed as a straight line

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