<p>I seriously get every single problem that involves the graph of a function wrong. I have no idea how to aproach them and they are keeping my score below 700. I have looked at the explanations on here and I still don't how their done. Any help would be greatly apreciated</p>
<p>pg.400 #18
pg.411 #13
pg.532 #8</p>
<p>Come on, someone please show me the way</p>
<p>Can you explain what you don’t get? Say what’s on your mind when you approach these problems (start with #18)</p>
<p>pg 400 #18
It’s bounded by the x-axis, the line x=4, and the graph of y=f(x).</p>
<p>The x-axis is the horizontal line at the bottom. It is labeled x.
The line x=4 is the vertical line to the right. It is above the 4 on the x-axis
The graph of y=f(x) is the curve of the shaded area. It is labeled y = f(x)</p>
<p>Do you understand this so far?</p>
<p>pg 400 #18 was a bad example, I understand that problem.</p>
<p>it’s like functions are a foreign language to me, I have zero understanding of them.</p>
<p>For example pg. 411 #13. h(x)=g(2x)+2, what is the value of h(1)? I have no idea how the answer is 3. Basically I need a crash course on functions and what they mean</p>
<p>^I don’t have the BB so I can’t help you there (although, h(1)=g(2*1)+2=g(2)+2. Presumably you know g(2), right?).</p>
<p>Anyways, functions. They are really an input-output machine. You input a value (generally, but not always, x). You output another value (generally, but not always, f(x) or, in other words, y). The function defines what one does to the input to get the output. Almost every graph you’ve seen is a function. This is true because you input your x value and output a y value. Using notation like f(x) is just a way to generalize functions when there is no graph. </p>
<p>Anyways, if your function is f(x)=3x+5 (which can generally also be written as y=3x+5), that means that you take any x input value, multiply it by 3, and add 5 to get your output f(x). So, f(2)=3*2+5=11. Here, your input is 2, and your output is 11. If you were to graph this, x would be your x-axis and f(x) would be your y-axis, so you’d have the point (2,11). To give you a similar function, g(a)=a^2-4 (remember, function inputs do not always have to be x and function outputs do not have to be f(x)). in this case, a is your input and g(a) is your output. g(a) is like f(a), except you are only using different letters. If you already have a function f(a), then your second, different, function can not be f(a) because that is a contradiction, as two different things can’t be represented by the same letters. So, you commonly use g to denote a second function, and h a third function, and so on. Anyways, if you input an a value of 0, so g(0)=0^2-4=-4, you get an output of -4. If you input an a value of 2, so g(2)=2^2-4=0, you get an output of 0. If you were to graph this, a would replace the x-axis and g(a) would replace the y-axis. You’d have the points (0,-4) and (2,0). </p>
<p>So, when you have two functions, like in your problem, you have to find two things. So, say you have a function f(a)=g(a^2)+5 and g(b)=3b. Say a=2. So, f(2)=g(4)+5. But, we need to know g(4) to solve the problem. Luckily, we know g(b)=3b. So, g(4)=3*4=12. Substituting that back in, we get f(2)=12+5=17. </p>
<p>Likewise, say you have a function h(r)=2<em>f(g(r)), where g(r)=3r+2 and f(s)=s^2. So, find h(3). h(3)=2</em>f(g(3)). g(3)=3<em>3+2=11 (because g(r)=3r+2). So, h(3)=2</em>f(g(3))=2<em>f(11). f(11)=11^2=121 (because f(s)=s^2). So, h(3)=2</em>f(11)=2<em>121=242. You could do this a more direct way by plugging the g function straight into the f function. In other words, h(r)=2</em>((3r+2)^2) by substituting 3r+2 in for g(r) (which is also s, when you think about it) and s^2 in for f(s). So, h(3)=2<em>((3</em>3+2)^2)=2<em>((11)^2)=2</em>121=242. Same answer. </p>
<p>^When it comes down to it, functions are really about book-keeping, especially when you have multiple functions in one problem. Even in problems with just one function, you have to sort the inputs from the outputs.</p>
<p>h(1) is the output value that you get when you input something.
y is the output value that you get when you input x.</p>
<p>THIS IS WHAT A FUNCTION IS. In “h(1)” h(x) is the function. as you can see 1 is the x-value</p>
<p>its like putting bread into a toaster to get toast</p>
<p>YOU PUT IN A VALUE FOR X TO GET A VALUE FOR Y.
THE VALUE FOR Y IS THE FUNCTION, f(x) or h(x) or h(1), etc.</p>
<p>basically a function is what you get (y-value) when you put in a number in an equation (x-value)</p>
<p>You can figure this out by looking at a graph or plugging the x into an equation</p>
<p>after you understand this, it’s just common math skills to finish the problem.</p>
<p>so for pg 411 #13,</p>
<p>when you’re given something like h(1), that means the x value is 1. The function of 1 is the y-value. Basically, the function of a specific number like h(1) is a point - (1, y). We need to figure out what y is by plugging in x.</p>
<p>the equation GIVEN in the problem is h(x) = g(2x)+2
So h(1) implies that the x-value of the point is 1.
therefore, h(1) = g(2*1)+2… you basically replace all the x’s with 1.</p>
<p>but now you have to find g(2), which is the y-value of the g(x) graph when x = 2.
looking at the graph, this is 1.
So, g(2) = 1
g(2)+2=3
h(1) = 3</p>
<p>so for pg 532 #8,</p>
<p>the question says f(b) = f(3)
you need to find a value of b that makes this equation true
obviously, b = 3 is ONE possible choice, but its not in the choices so you have to find ANOTHER value of b that satisfies the equation.</p>
<p>AS SAID BEFORE, the FUNCTION of anything is the y-value, and what is in the parantheses is the x-value.
So, f(b) = f(3)
When you put in b, you get the same y-value as you get when you put in 3.
When you put in 3, or when the x-value in the graph is 3, you get 5 (count the squares).
When you put in b, or when the x-value in the graph is 3, you get 5 (count the squares).
Find b for yourself</p>
<p>*** think about it like a graph. How do you find a point? You go to the x-value, then move up until you hit the y-value.
This is the same as a function. When you put in an x-value in an equation, you get the y-value, or f(x)</p>
<p>If
f(x) = x+1 was graphed, to find f(4), you put in 4 in the EQUATION, making…
f(4) = 4+1
f(4) = 5
As you can see, since the f(x) is the y-value, and it is equal to 5, y is 5.
So, the point (4,5) is 1 point on the graph</p>
<p>Thank you soooooo much for these responses, they were exactly what I was looking for</p>