Hello,
I am a perfect math dunce and I need some help on a couple of questions.
For which of the following functions is
f(-3) > f(3)
A ) f(x) = 4x squared
B) f(x) = 4
C) f(x) = 4 over x
D) f (x) = 4 - x to the third power
E) f(x) = x to the forth power + 4
I will post the other question later - I am going to see if I can insert a picture.
Thanks!
Let’s examine each of the cases individually.
A) 4x^2 - the even exponent 2 tells us we have the same answer (same sign, +ve). so f(-3) = f(3)
B) The value of this one is ALWAYS four, because this is a constant function. (horizontal line) so again, f(-3) = f(3)
C) f(-3) gives us a -ve answer, and f(3) gives us a +ve answer. so f(-3) < f(3), the opposite of what we need to find.
D) Now we have an ODD exponent of 3 - this tells us that once we substitute (-3), we’d have a great negative number. But this number would be preceded by the - sign originally in the equation. So --= +. However, for f(3), we’d have -+ (because 3 is a positive number, so positive answer * the minus sign).
Since for f(-3) we have addition and f(3) we have subtraction, f(-3) is definitely > f(3). This is our answer.
E) fourth power = always a +ve answer (even exponent), so again, f(-3) = f(3).
Keep in mind these notes, and you’d reach the answer very quickly:
constant function - always same y.
x to the power of an even exponent - always same answer. (assuming we substitute x and -x)
x to the power of an odd exponent - sign varies. (assuming we substitute x and -x)
Another way is to substitute both 3 and -3 in each of the choices, but this way is time consuming.
The second way may atcually prove not that labor/time intensive if you let the brute force of TI calculator do all the dirty work.
TBLSET: TblStart=-3, /\Tbl=1, Auto, Auto. As the famous infomercial’s line goes, set it and forget it. (You youngins probably don’t even know this classic one. 
)
A) Y1=4x^2, TABLE - compare Y1 in the top and the bottom lines (for x=-3 and x=3). 36=36. Rinse and repeat.
B) Y1=4, TABLE, 4=4. Duh!
C) Y1=4/x, TABLE, -1.333<1.333. Move along, folks.
D) Y1=4-x^3, TABLE, 31>-23. THE END.
We could set /\Tbl=6 and compare the Y1 values in the top 2 lines, but why think?
We could also learn and/or memorize all the esoteric functions’ properties (see the nimble @BethanyD’s mindworks^), but that’s, in two words, BORE-RING!
Let’s combine math and CR.
The correct answer is (E).
When I wrote bore-ring (capitalized!), I meant quite the opposite: learning and applying math is fun.
clarifying just in case
Hey @HeLives98, even though you self-deprecatingly said “I am a perfect math dunce”, this short explanation may entice you to read up on functions’ graphs and properties.
The simplest scenario for f(-3) > f(3) happens when f(x) is strictly decreasing for all x (see the link below).
A quick scan of all the answer choices reveals that (D) 4-x^3 is the one.
Here’s why. The graph of y=x^3 is increasing; flipped over the x-axis it becomes decreasing y=-x^3; shifted up 4 to get y=4-x^3 - still decreasing. Done.
Of course, we got lucky, and the right answer could be, for example, some polynomial of third or higher degree, but why be gloomy in advance?
The promised link: [Math is fun.](Increasing and Decreasing Functions)
Probably the easiest approach for someone who doesn’t love math is to use your graphing calculator.
Graph each of the four choices.
Then find f(-3) and f(3). You can do it visually— look and see where the graph is when x = -3 as opposed to x=3. Or you can let the calculator give you the answers. (On the TI 84: 2nd, trace, choice 1- value. Enter x=-3, enter, then x=3 enter and compare.)