All are the equations functions?

Question

Explain

With regards

Answer 1

a function has some input and has one or many output...

an equation is just an expression

In many cases a function can be expressed in terms of some equation...

but the inverse is not true...
for example

a^2 + b^2 + c^2 + d^2 = e^2 + f^2 + g^2 + h^2 is an equation (EQ1)
but not a function

but consider the case
"a" is a function of b,c,d,e,f,g,h
a = f(b,c,d,e,f,g,h,i,j)
= sqrt(e^2 + f^2 + g^2 + h^2 -(b^2 + c^2 + d^2))

so,
a = sqrt(e^2 + f^2 + g^2 + h^2 -(b^2 + c^2 + d^2)) ... ... ... ... (EQ2)
is a function expressed as a equation...

here inputs are b,c,d,e,f,g,h,i,j
and output is "a"

EQ1 is not a function
EQ2 is a function

Answer 2

no,
the equation for a circle such as x^2 + y^2 = r^2 is an equation but it isnt a function since it doesnt pass the vertical line test. in the equation x^2 + y^2 = 25, if x = 0 then y could equal both 5 and -5. for an equation to be a function there has to be a 1-to-1 relation from the domain to the range.

Answer 3

Not all equations are functions.

An equation is essentially some algebraic expression with an equals sign in it... where one side equals another. This is in contrast to INEQUALITIES which are algebraic expressions without equals signs where one side is greater than the other or some such...

Equations may be used to solve for an unknown...

let x be the unknown

ummm... (2x + 7) = 15 or some such... and you have an equation.

A FUNCTION is a TYPE of equation where the a parameter (eg x) is used to find out the function of the parameter... these classically can be graphed.


f(x) = 2x + 7 graphs out to a straight line with slope 2 and y interecept -7

f(x) = x^2 graphs out to a parabola...

this sort of thing. Functions are a subset of equations.

Answer 4

definitely not..

i have learned that not all equations are functions.
that's basic..
if the equation did not passed the vertical line test, it's not a function..

like for the equations of circles and ellipse..
definitely it's an equation, but not a function.

Answer 5

In a single independent variable, a function must have 1 unique dependent variable value mapped to a given independent variable value. Not so with all equations.

Answer 6

Not all equations are functions.

Answer 7

not all equations are functions

Answer 8

no

Answer 9

no