<p>If f(a)=a^2+7 for all real values of "a", which of the following values is a possible value of f(a)?</p>
<p>a)-2
b)0
c)Square root of 5
d)Square root of 7
e)100*square root of 3</p>
<p>The domain is all real #s and it asks for all real values, which is a possible value. The value of a function is always the Y(same thing as f(x). The answer came out to be E even though any other one would work. But is this question saying that the value would have to be greater than 7? It will in the end, but what you choose for "a" is supposed to be greater than 7? Why though? All other values work. But is it saying that in the end, what is one possible value that is in the range? It's not asking you to plug in for "a", rather what would be the outcome? Because in this case, -2 isn't possible. If this is the case and the right concept, how do you always differentiate between the two?</p>
<p>Yes that is the whole question, but now that I think about what my calculus teacher said, maybe it does make sense. The value of the equation is the Y, aka f(x), aka the end result of the equation. So if there is to be an end result of this equation, it has to be greater than 7 because you square any #(making it positive and greater than 0). I always thought it related to plugging in, not the value. Sometimes you need to do these questions quickly to get good scores(for 700+, you need to do easy quickly), but reading it quickly can make your answer wrong. Thanks amb3r for your insight(late but helped me a little). </p>
<p>Another question: A team played 162 baseball games and won 62 more than it lost. How many games did it win?</p>
<p>a)100
b)104
c)108
d)112
e)116</p>
<p>Why could you just say the # they lost was X, and the number they won was X+62, add them up and set it equal to 0: 2x+62=162 and get 100? That's not the answer. Instead, the appropriate method was to say the # of wins is X and the # of losses is X-62 and you get 2x-62=162 to get 112. Why does the first method not work? I could plug in but the studyguide I'm using is saying that sometimes you gotta know to use either substitution, plugging in, or algebra. If I can remember the algebra ways to do these problems, then I'm good to go, but I have to know why they work the way they do.</p>
<p>I think my mind was thinking that I subtracted 62 to get 100 and I sort of knew I was doing something wrong because that equation seemed right but I didn't think it through, somehow the 2X=100 didn't complete and it seemed like 100 remained and the thought of 162-62=100 being a trap and my mind stopped working after the word trap came to mind. Either way, I'm plugging in on these most of the time but knowing the equations in advance is helpful, unless I think it quickly enough on the SAT.</p>
<p>To Kevin, is there any way that this equation could ever equal 0? Not a chance. I did the same mistake as you by plugging in those #s. Values(what I said)=y=f(x)=end result of the equation. I wouldn't even know what to do if I were clueless and had to guess on that because they all seem so innocent correct!</p>