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Evaluation:
Evaluating Expressions, "Evaluation" mostly means "plugging numbers in for variables, and simplifying". Sometimes they just give you the numbers, and want you to simplify, which is more of an order-of-operations kind of question. In this lesson, I'll concentrate on the "plug and chug" aspect of evaluation: plugging in values for variables, and "chugging" my way to the simplified answer. Usually the only hard part in evaluation is in keeping track of the minus signs. I would strongly recommend that you use parentheses liberally, especially when you're just getting started. Here are some typical examples:
Just plug in the given values, being careful to use parentheses, particularly around the minus signs: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved (–2)2(3) = (4)(3) = 12
(–2) – (–4)(4) = –2 – (–16) = –2 + 16 = 16 – 2 = 14
Don't try to "distribute" the exponent through the parentheses. Exponents do NOT distribute over addition! Do NOT try to say that (b + d)2 is the same as b2 + d2! They are NOT the same thing!! Just evaluate the expression as it stands: ( (3) + (4) )2 = ( 7 )2 = 49
(3)2 + (4)2 = 9 + 16 = 25 Notice that this does not match the answer to the previous evaluation!
(3)(–4)3 – (–2)(4) = (3)(–64) – (–8) = –192 + 8 = –184 The most common "expression" you'll likely work with will be polynomials. To evaluate, you take the polynomial and plug in a value for x.
(–3)4 + 3(–3)3
– (–3)2 + 6
3(–2)2 – 12(–2) + 4 = 3(4) + 24 + 4 = 12 + 24 + 4 = 40
y = 4(–1) – 3 = –4 – 3 = –7 Note: This means that the point (–1, –7) is on the line y = 4x – 3.
y = 4(0) – 3 = 0 – 3 = –3 This means that (0, –3) is on the line.
y = 4(3) – 3 = 12 – 3 = 9 Then (3, 9) is on the line.
You can verify that the points I found (by evaluating the equation y = 4x – 3) are on the graph by checking that (–1, –7), (0, –3), and (3, 9) are all on the blue line. You will also need eventually to evaluate functions. For the following exercises, let
To evaluate a function, do just what I did above:
plug in the given value for x.
Here, you are supposed to evaluate at the value x
= –3. The notation is different, but "f(–3)"
means exactly the same thing as "evaluate
Note how I used parentheses. It is very easy to mess up the minus signs if you're not careful and use lots of parentheses. Take the time to be careful!
Note that I gave the answer in two formats: the "exact" form (with the radical in it) and the "approximate" form (with the wiggly "equals"). Usually you will be expected to evaluate exactly; that is, it will usually be correct to leave the answer in a messy form (with a radical, or a fraction, or with pi in it [instead of rounding to 3.14], etc). However, there are times when the approximate form is better. Often, word problems need an answer that can be applied in "real life". For instance, "square root of 24 meters" isn't very useful when you're trying to figure out what length to cut a board to, but "about 4.9 meters" is perfectly useful, and probably quite accurate enough for whatever you're building. You will also need to approximate for when you're graphing. For instance, I would have no idea where to plot the square root of 24, but I know right where to draw the line for 4.9. By the way, you graph functions just like you graph other equations: by evaluating the function at a few values of x, drawing the points, and connecting the dots. (This is exactly what a graphing calculator does, by the way.) Here's what this function looks like:
Just remember: "evaluate" means "plug-n-chug". Be careful with the subtractions, negatives, and exponents (by using parentheses appropriately). Don't try to do too much at once; don't skip steps, don't try to do three steps at once, and don't try to do everything in your head. Take your time, and evaluation problems should work out fine!
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Copyright © 2006-2008 Elizabeth Stapel | About | Terms of Use |
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at x = –3"!
