I hate functions!!!!

Test Preparation SAT Preparation
1

<p>I have tried to understand functions but I continue to get problems wrong. I have been practicing in the BB and using workbooks, but, again, I continue to get questions wrong. I JUST DO NOT UNDERSTAND WTH FUNCTIONS ARE AND WHAT "K AS A CONSTANT" MEANS.</p>

<p>I got the following function problems wrong. </p>

<pre><code> pg.367-#3
</code></pre>

<p>The question is For which of the following graphs of f does f(x)=f(-x) for all values of x as shown.
CANT DRAW THE GRAPHS HERE</p>

<pre><code> pg.369-#8
</code></pre>

<p>The figure above shows a portion of the graph of the function f. If f(x+5)=f(x) for all values of x, then f(x)=0 for how many different values of x between 0 and 12?
A. Eight
B. Nine
C. Ten
D. Eleven
E. Twelve</p>

<pre><code> pg.370-#10
</code></pre>

<p>According to the table above, if k=f(3), what is the value of g(k)?
CAN'T DRAW THE TABLE
A. 1
B. 2
C. 3
D. 4
E. 5</p>

<pre><code> pg. 418-#18-
</code></pre>

<p>The graph above shows the function g, where g(x) = k(x+3)(x-3) for some constant k. If g(a-1.2)= 0 and a>0, what is the value of a?</p>

<pre><code> pg. 465#7
</code></pre>

<p>The graph above is a parabola whose equation is y=ax^2 + 2, where a is a constant. If y=a/3x^2 + 2 is graphed on the same axes, which of the following best describes the resulting graph as compared with the graph above?
A. It will be narrower
B. It will be wider
C. It will be moved to the left
D. It will be moved to the right
E. It will be moved 3 units downward</p>

<pre><code> pg. 340-#15
</code></pre>

<p>The graph above is a parabola that is symmetric about the x-axis. Which of the following could be an equation of the parabola?
A. x = y^2- 2
B. x = -y^2 - 2
C. x = (y-2)^2
D. x = (y- root2)^2
E. x = -(y-root2)^2</p>

<pre><code> pg. 350-#19
</code></pre>

<p>The figure above shows the graph of y=k-x^2, where k is a constant. If the area of triangle ABC is 64, what is the value of k?</p>

<pre><code> pg.424-#16
</code></pre>

<p>PLEASE LOOK IN THE BB!</p>

<p>If you guys would please help me with understanding these problems and functions as a whole I would REALLY REALLY appreciate it. I thank those in advance who will put their time and effort into helping me understand these problems. :)</p>

2

<p>p 367-- so in a function, f(x) is the same thing as saying “y”. f(x) is the output when you put x into the function. So if you have the equation f(x)=3x+1, f(3) = 3(3) + 1 = 10. so f(3) = 1. When it says f(x)=f(-x), it’s asking which graph shows that the result of putting in “x” is the same as putting in “-x”. An example would be f(x) = |x| (absolute value) or f(x)=x^2. So just find the graph that’s symmetrical with respect to the y-axis.</p>

<p>p 369–again, f(x) is the output. So when it says f(x+5) = f(x), it means that the output for one number is the same output as the output for that number plus 5. Eg. f(3) = f(8). When it says f(x) = 0, it means that the output for x is 0. So this question is asking for a function where for all values of x (which means all the time), the output is the same as the output for 5 in front of it, and that the output is 0. In other words, it’s looking for a straight line at y = 0.</p>

<p>p 370-- k = f(3), g(k) = ? So, again, anything in the form y(x) (a letter followed by a number/variable in parentheses) is function notation. They use different letters for different equations. So maybe f(x) = 3x, g(x) = x-12 (or something like that.). So in this case, some number “k” is the same thing as the output of f(x) when the number 3 is put into the equation. Look at the chart, and look for f(3). That’s what k equals. Then look for the section of the chart that describes g(x). Find where it says g(k). (so if k = 4, then look for g(4))</p>

<p>p 418-- It’s harder here, since I can’t see the graph, but here goes. It gives you the fact that g(a-1.2) = 0, so when you plug in (a-1.2) wherever you see “x”, then the result will be 0. Let me try and show you
g(x) = k(x+3)(x-3)
g(a-1.2) = 0<br>
g(a-1.2) = k ((a-1.2) + 3)((a-1.2) - 3) = 0 (substitute)
0 = k (a + 1.8) ( a - 4.2) (simplify)
0 = (a + 1.8)(a - 4.2) (divide by k)
so
(a + 1.8) = 0 or (a - 4.2) = 0
so
a = -1.8 or a = 4.2
and since a >0, it can’t be -1.8, so a = 4.2</p>

<p>p 465-- So this has to do with transformations. It’s sort of complcated to show here, but I’ll do my best.<br>
If anything happens in parentheses with the x, it’s going to affect the horizontal. Anything outside of parentheses with the x is going to be vertical.
Multiplication is going to mean a stretch or compression. If it’s horizontal, if it’s multiplied by a number less than 1, it’s going to be a horizontal stretch. Greater than one will be a compression. If vertical, it’s backwards.
If multiplied by -1, it’s going to be a reflection over one of the axes.
Addition and subtraction will just shift the graph around. If horizontal, addition will move left, subtraction will move right. If vertical, addition will move up, subtraction will move down.
So
In this example, it has been multiplied by some number (a/3) and 2 has been added. Because none of them are in parentheses with the x, both will affect the vertical. the +2 will shift the graph up 2 units. the a/3 will either stretch or compress the graph vertically (making it “taller” or “shorter”) depending on if a/3 is less than or greater than 1. I would assume that it will be a stretch, but think about it and look at the graph–maybe you’ll see it better than I can. :D</p>

<p>p 340 – so symmetric about the x axis means it’s line of symmetry is the x axis. By now, you should be able to graph basic parabolas, and I just discussed the transformations. These are all sideways parabolas (they’re x=y^2, not y = x^2), so all the transformations are backwards here. Everything I taught you in that earlier question is backwards for sideways parabolas. Just take the time and draw a rough sketch with the transformations, and see what you come up with.</p>

<p>p 350 – Okay, I’m assuming I’m missing some sort of picture of triangle ABC here, because I can’t solve it like this. And I don’t have a book. Sorry :(</p>

<p>PM me if you have any other questions or still need help! I hope this helped a little. :)</p>

3

<p>I can totally relate to hating functions. If mathematicians had gotten together with the goal of creating the most confusing method of graphing, they couldn’t have done much better than functions. </p>

<p>Remember that functions are graphs, and on many you’ll be given the x-value and asked to find the y-value, or vice-versa. Let’s go through a couple problems. We’ll start with something basic:</p>

<p>If y = f(x), and f(x) = 3x + 8, what is f(2)?</p>

<p>Since y = f(x), you can substitute y for f(x), and you have y = 3x + 8.
When the question asks, what is f(2), it’s asking for y when x is 2. It’s giving you the x-value and asking for the y-value. Just plug in 2 for x:
3(2) + 8 = 14</p>

<p>Contrast that with the question below:</p>

<p>If f(x) = 5x -3, and f(k) = 12, what is k? </p>

<p>Now you’re being given a variable in place of x, so you have 5k - 3, which doesn’t help us all by itself. But we’re given that f(k) = 12, which means that 5k - 3 = 12. Now we can solve for k:
5k -3 = 12
k = 3 </p>

<p>Whatever replaces the x in parenthesis should replace the x on the right side of the equation. If you’re given a number, as you were on the first example, you’re being given the x-value, so just substitute that value for x. If you’re given a variable in place of x and what that equals, such as f(k) = 12, you’re being given the y and need to find x. </p>

<p>Even when questions get more complicated, you still follow the same rules:</p>

<p>If f(x) = 3x - 5 and g(x) = 8x + 10, what is the value of f(k) if g(k) = 2? </p>

<p>This problem may seem difficult, but it’s really just a combination of smaller steps. We need to find f(k), so we need the value of k.
We’re given that g(k) = 2, so we can use the formula for g(x) to find k:</p>

<p>If g(k) = 2, and g(x) = 8x + 10, then 8k + 10 = 2
k = -1</p>

<p>Then plug in -1 for k in f(x):
3(-1) - 5 = -8</p>

<p>I find that some of my students need to go over the rules of functions five or six times before it clicks. It may frustrate you, but you’ll get there eventually. </p>

<p>I haven’t addressed all your function issues, but this is a good place to start for someone who hates functions. You can also hear a different explanation here:
[Introduction</a> to functions | Khan Academy](<a href=“Khan Academy”>Khan Academy)</p>

<p>I hope this helps.</p>

4

<p>Boy, today must be “I hate functions” day. (Or is that everyday?) I just finished emailing someone else about this. I’m posting a section from “The New Math SAT Game Plan” that I hope will help…</p>

<p><a href=“http://mysite.verizon.net/vze8kuaf/pland/gameplan%20functions.pdf[/url]”>http://mysite.verizon.net/vze8kuaf/pland/gameplan%20functions.pdf&lt;/a&gt;&lt;/p&gt;

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<p>^ It kinda did help. It cleared some misconceptions I had. Thanks.</p>

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<p>^I’m glad to hear it. If you still have any questions, just post them…</p>

7

<p>This is weird, I was just thinking about how much I love functions haha. They remind me so much of Computer science programming. Although, I will agree that the SAT does insist on butchering their purpose in their stupid convoluted questions.</p>

8

<p>I used to hate functions, but now I’m getting pretty good at them. Now I hate 3 dimensional geometry questions. :(</p>

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<p>^ i really really hate those!! :)</p>

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<p>Here in 2014 I just came across this problem “The graph above shows the function g, where g(x) = k(x+3)(x-3) for some constant k. If g(a-1.2)= 0 and a>0, what is the value of a?” And found that <a href=“http://sat.magoosh.com/forum/4363-the-graph-above-shows-the-function-g-where”>http://sat.magoosh.com/forum/4363-the-graph-above-shows-the-function-g-where&lt;/a&gt; has a great quick and simple explanation! </p>

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<p>Don’t hate functions. I have books entirely on functional equations or functional analysis.</p>

<p>The biggest thing with functions on the SAT is, don’t let the notation scare you. For example, if f(x) = x^2 + 1 and it tells you to evaluate f(f(3)), just think of it as f of f(3), so f(f(3)) = f(10) = 101, done.</p>

<p>Some functions problems are a little trickier, take the following example:</p>

<p>If f(3x+1) = x^2 for all values of x, find f(7).</p>

<p>Clearly the answer is not 49 (f(22) = 49). Instead, letting x = 2 gives f(3*2 + 1) = 2^2, or f(7) = 4.</p>