Linear equations are always functions.
Assuming you work with two variables (like x and y) only: if the graph is a vertical line, e.g. x = 5, then it is not a function. Otherwise it is.
There is one form of linear equation that is not a function, and that is when x = c, where c is a constant.
yes, a vertical line is linear, but it's not a function.
In some cases, a knowledge of the function in question helps. For example, when you have multiple equations, if you have more equations than variables you will usually have infinite solutions. Another example is that certain functions are known to be periodic, for instance the trigonometric functions - so an equation such as sin(x) = 1/2 may have infinite solution, due to the periodicity.
There are many linear equations that equal 91! For instance, 2x + 4 = 91 and 3x + 5 = 91 Too many equations.. The question needs revision!.
This can happen in different ways: a) More variables than equations. For instance, a single equation with two variables (such as x + y = 15), two equations with three variables, two equations with four variables, etc. b) To of the equations describe the same line, plane, or hyper-plane - this, in turn, will result in that you "really" have less equations than it seems. For example: y = 2x + 3 2y = 4x + 6 The second equation is simply the first equation multiplied by 2.
Equations are said to be equivalent if they have the same solution. This definition also holds true in rational equations or equations involving rational expressions. For instance, the equations 2x = 14 and x - 3 = 4 are equivalent. Why? It's because they have the same solution, that is x = 7.
Yes, a vertical line is linear, but it is not a function, because every point on the line has the same x value.
These are equations to calculate reference values for pulmonary function testing. The parameters are for instance TLC (Total lung capacity), VC (vital capacity), FRC (functionnal residual capacity) etc...
If an equation is a function, then:The set of coordinates doesn't consists of the same first member. For instance, the set can't contain (1,2) and (1,1).There exists only a function within the specific interval. For instance, f(x) = x within -1 ≤ x ≤ 1 and x + 2 within 1 < x ≤ 3. If f(x) = x and x + 2 within -1 ≤ x ≤ 1, then this doesn't make an equation the function.
It means you should rearrange the equation so that x is on one side of the equal sign, and everything else on the other, with no "x" on the right side of the equation. For instance, if I was told to express x as a function of y and given the equation: x-4y=6 I would express x as a function of y by rearranging the equation to read: x = 6+4y
No. To understand how friend functions relate to static functions you first need to understand the three qualities of a normal member function (an instance member function): 1. The function has access to the private aspects of the class in which it is declared. 2. The function is scoped to that class. 3. The function must be invoked on or from within an object of that class. A static function only has the first two qualities (so no instance of the class is required) while a friend function only has the first quality (so is neither scoped to the class nor requires an instance of the class). All three share the first quality only but that alone does not make them similar. It is the qualities they lack that sets them apart.