i need help with my homework

Question

f(x) = x^2 - 3x  find f(-8)

 

P(T)=4t -5 Find P(T-2)

W(N) = 4n+2 Find W(3n)

G(A)=3^3a-2: Find G(1)

G(X) =3x -3 : Find G(-6)

H(T) =2times 5^-t-1. Find H(-2)

G(A)=4a: Find G(2a)

W(A)=a+3: Find W (A+4) 

Answer 1

1.  If given f(x) = x² - 3x then find f(-8).
     Substituting -8 for x we get (-8)² - 3(-8), which gives us 88.

2.  If given p(t) = 4t - 5 then find p(t - 2).
     Substituting t - 2 for t we get 4(t - 2) - 5, which gives us 8t -13.

3.  If given w(n) = 4n + 2 then find w(3n).
     Substituting 3n for n we get 4(3n) + 2, which gives us 12n + 2.

4.  If given g(a) = 3^3a-2 then find g(1).
     Substituting 1 for a we get 3^{3(1) - 2}, which gives us 3¹ or simply 3.

5.  If given g(x) = 3x - 3 then find g(-6).
     Substituting -6 for x we get 3(-6) - 3, which gives us -21.

Answer 2

Here's another explanation of what the heck functions even are that will hopefully make sense to you.

Okay, so the first thing to remember is that we're dealing with graphs here.  Your basic algebraic equation like y = mx + b is the equation of a straight line.  No matter what's on the right side of the equation, though, it corresponds to some sort of graph, whether that be a parabola or anything else.  Basically, what we're saying when we change the "y" to "f(x)" is that the x and y values of any given point on that line will share the same relationship to each other no matter what.  For any x value you want to work with in this equation, you can use the same exact rule to determine the corresponding y value.  

For example, y = 3x means that for any value you pick for x, the y value will be three times that much.  The term "f(x)" actually means "the function of x" or to put it another way, "the value of y in terms of x".  The whole "f" thing doesn't really matter, it can be any placeholder letter you want and still make sense.  That's why some of your problems involved things like "W(N)" and "G(A)".  The actual letters don't matter at all; it's just a math way of saying that the y value will be written in terms of the variable inside the parentheses.

You can think of functions as a little machine on your page.  If your machine is "f(x) = 3x + 4", then that means that if you start with an x and you want to end up with the y that goes with it, you can just plug the x into the 3x + 4 machine and you'll come out with the matching y.

Let's take the first problem as an example.  Your first machine is f(x) = x^2 - 3x, and they want you to find f(-8).  That just means they've handed you the value "-8" for your starting x, and they want you to put it in the machine and see what comes out.  So you substitute -8 for any x values in the machine's rule, which is x^2 - 3x.  You'll end up with:

(-8)^2 - 3(-8)

which will work out to

64 - (-24)

64 + 24

88

So you've used the function machine to find the corresponding y value for when x is -8.  That's it!

I hope this helped!

 

Answer 3

Answering this one also answers your other question.  Simply substitute -8 wherever there is an x and simplify.

f(-8) = (-8)² - 3(-8)

-8² is 64, and -3 * -8 is 24, so your answer is:

f(-8) = 88

With this information, you should be able to work your other problem on your own.  :)