Y = x2
When you see the actual function (e.g. f(x) = ...) you can know what each input corresponds to, and can construct any table. If you are given just the table, you cannot always predict the function correctly, since the function the table seems to represent does not necessarily have to be that function. For example, it might seem that x : f(x) -2 -4 -1 -2 0 0 1 2 2 4 would correspond to f(x) = 2x, but this is not necessarily the case. There could be some arbitrary function that just happens to contain those five points.
If those are the only values, no.
A huge number. 0 + 1 + 2 = 3 0 + 2 + 1 = 3 1 + 0 + 2 = 3 1 + 2 + 0 = 3 2 + 0 + 1 = 3 2 + 1 + 0 = 3 -0 + 1 + 2 = 3 -0 + 2 + 1 = 3 1 - 0 + 2 = 31 + 2 - 0 = 32 - 0 + 1 = 32 + 1 - 0 = 3 0 - 1 + 3 = 2 0 + 3 - 1 = 2 -1 + 0 + 3 = 2 -1 + 3 + 0 = 2 3 + 0 - 1 = 2 3 - 1 + 0 = 2 -0 - 1 + 3 = 2-0 + 3 - 1 = 2-1 - 0 + 3 = 2-1 + 3 - 0 = 23 - 0 - 1 = 23 - 1 - 0 = 2 0 - 2 + 3 = 1 0 + 3 - 2 = 1 -2 + 0 + 3 = 1 -2 + 3 + 0 = 1 3 + 0 - 2 = 1 3 - 2 + 0 = 1 -0 - 2 + 3 = 1-0 + 3 - 2 = 1-2 - 0 + 3 = 1-2 + 3 - 0 = 13 - 0 - 2 = 13 - 2 - 0 = 1 1 + 2 - 3 = 0 1 - 3 + 2 = 0 2 + 1 - 3 = 0 2 - 3 + 1 = 0 -3 + 1 + 2 = 0 -3 + 2 + 1 = 0 For each of these equations there is a counterpart in which all signs have been switched. For example 0 + 1 + 2 = 3 gives -0 - 1 - 2 = -3and so on. Now, all of the above equations has three numbers on the left and one on the right. Each can be converted to others with two numbers on each side. For example:the equation 0 + 1 + 2 = 3 gives rise to0 + 1 = 3 - 20 + 1 = -2 + 30 + 2 = 3 - 10 + 2 = -1 + 31 + 2 = 3 - 01 + 2 = -0 + 3-0 + 1 = 3 - 2-0 + 1 = -2 + 3-0 + 2 = 3 - 1-0 + 2 = -1 + 31 + 2 = 3 + 01 + 2 = +0 + 3 As you can see, the number of equations is huge!
Removing one pair is not enough to make it a function. You need to remove one of the pairs starting with 1 as well as a pair starting with 2.
1 1/2
x| -1 | 0 | 1 | 2 | 3 y| 6 | 5 | 4 | 3 | 2 what function includes all of the ordered pairs in the table ?
y = 1/2 x + 1
When you see the actual function (e.g. f(x) = ...) you can know what each input corresponds to, and can construct any table. If you are given just the table, you cannot always predict the function correctly, since the function the table seems to represent does not necessarily have to be that function. For example, it might seem that x : f(x) -2 -4 -1 -2 0 0 1 2 2 4 would correspond to f(x) = 2x, but this is not necessarily the case. There could be some arbitrary function that just happens to contain those five points.
The table shows ordered pairs for a polynomial function, f х f(x) -3 63 --2 8 -1 - 1 0 0 1 -1 2 8 3 63 What is the degree of f?
Input (g) Output (h) 0 0 1 7 2 14 3 21 ...and so forth.
The simplest way to describe this action is to demonstrate using a simple truth table. This is not intended to be an in depth study of the theorms but a simple demonstration of how a trivial equation can be demorganized. Given a simple boolean equation !A+!B=1. One could show in a truth table. !A !B !A+!B (fully inhibited OR function) 0 0 1 0 1 1 1 0 1 1 1 0 Demorganizing (hypersimplified method) 1) NOT all variables 2) NOT the equation 3) Invert the function (AND to OR or OR to AND) Iterative steps yeilds !A becomes !!A which is the same as A (!!A + !B) = (A+!B) !B becomes !!B which is the same as B (A +!!B) = A+B OR function becomes AND (A+B) = (AB) NOT the full equation !(AB) = !A+!B Truth table for the new equation (which happens to be a NAND function) A B AB !AB !A+!B 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0
no
(2, 4)
yes
Yes. A quadratic function can have 0, 1, or 2 x-intercepts, and 0, 1, or 2 y-intercepts.
The unit step function at t=0 is defined to have a value of 1.
1000 in base 2 equals 8 in base 10. To work this out do a conversion table is the easiest method. So set up 1, 2, 4, 8 (2^0, 2^1, 2^2, 2^3) Now fill in the table by lining it up, eg. 1 = 8, 0 = 4, 0 = 2, and 0=1. Now add the answer up and it equals 8 + 0 + 0 + 0 = 8.