Function Notation and Evaluation smashville247.net Topical outline | Algebra 1 summary | MathBits" Teacher resources Terms that Use call Person: Donna Roberts

Function notation is the method a function is written. It is meant to it is in a precise way of providing information about the role without a rather an extensive written explanation.

Traditionally, attributes are described by single letter names, such as f, g, h and for this reason on. Any kind of letter(s), however, may be supplied to name a function. Examples:


The f (x) notation is another method of representing the y-value in a function, y = f (x). The y-axis may even be labeled as the f (x) axis, when graphing. notified pairs might be created as (x, f (x)), rather of (x, y).

The most popular duty notation is f (x) i beg your pardon is read "f that x". This is not the multiplication of f times x.

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Note: The notation f : X Y tells us that the function"s surname is "f " and its ordered pairs are developed by an element x indigenous the collection X, and also by an element y native the set Y. (The arrow is review "is mapped to".)
it permits for individual duty names to prevent confusion regarding which duty is being examined. names have different letters, such together f (x) and g (x). The graphing calculator walk distinctive function naming v Y1, Y2, ...
it quickly identifies the independent change in a problem. f (x) = x + 2b + c, where the change is "x".
it conveniently states which element of the role is to it is in examined. Find f (2) when f (x) = 3x, is the same as saying, "Find y as soon as x = 2, for y = 3x."
(the bar arrow way the facet "x is mapped/matched come 3x + 2")



To evaluate a function, instead of the entry (the provided number or expression) for the function"s change (place holder, x). replace the x v the number or expression.
Given the function f (x) = 3x - 5, uncover f (4). Solution: instead of 4 into the function in place of x. f (4) = 3(4) - 5 = 7. This answer can be assumed of together the bespeak pair (4,7). The answer may also be referred to as the picture of 4 under f (x).
Find the worth of h (b) = 3b2 - 2b + 1 once b = -3. Solution: Substitute -3 right into the role in ar of b. h (-3) = 3(-3)2 - 2(-3) + 1 = 34.
Find g (2w) when g (x) = x2 - 2x + 1. Solution: When substituting expressions, like 2w, right into a function, using parentheses will help prevent algebraic errors. Because that this problem, usage (2w). g (2w) = (2w)2 - 2(2w) + 1 = 4w2- 4w +1 (Note: the prize is in regards to w.

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Solution: Be certain to usage parentheses! Be cautious - much more algebra work-related is necessary here. f (2a + 3) = 2(2a + 3)2 + 4(2a + 3) - 3 = 2(4a2 + 12a + 9) + 8a + 12 - 3 = 8a2 + 24a + 18 + 8a + 12 - 3 = 8a2 + 32a + 27
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Given f (x) = x2 - x - 4. If f (k) = 8, what is the value of k? Solution: Set the function rule same to 8 and solve for k.