Functions on a Cartesian Plane

Key Questions

• How do you plot a function on a cartesian plane?

  Answer:

  There is a procedure to graph a function.

  Explanation:

  • Define the domain and codomain

  • Find the intersection between function and x-axes:
    solve `f(x)=0`

  • Calculate the first derivative and its intersection with x-axes:
    `f'(x)=0`. This points are called extrema, geometrically represent the points where the tangent of the function is horizontal. This mean that the function reach its minimum or maximum or stationary points.

  • Calculate the second derivative and its intersection with x-axes:
    `f''(x)=0`. This points (inflection point) are points on a curve at which the curve changes from being concave to convex or vice versa.
    if `f''(x)>0` the function is convex (is smiling)
    if `f''(x)<0` the function is concave (is sad)

  Some typical example of domain.

  AltairSafir · 1 · Apr 21 2018
• What does `(x,y)` mean?

  Answer:

  See explanation below

  Explanation:

  `(x,y)` is a pair of real numbers. The meaning is:

  `(x,y)` is an ordered pair of numbers belonging to `RRxxRR=RR^2`. The first pair memeber belongs to the first set `RR` and the second belongs to second `RR`. Althoug in this case is the same set `RR`. Could be in other cases `RRxxZZ` or `QQxxRR`

  `(x,y)` has the meaning of an aplication from `RR` to `RR` in which to every element x, the aplication asingns the y element.

  `(x,y)` has the meaning of plane's point coordinates. The first x is the horizontal coodinate (abscisa) and second is the vertical coordinate (ordenate). Both are coordinates.

  `(x,y)` has the meaning of a complex number: x is the real part and y is the imaginary part: `x+yi`

  `(x,y)` has the meaning of a plane's vector from origin of coordinates

  etc...

  You will see that meaning of `(x,y)` could be whatever of above depending of context, but if you think a little bit, all meanings are quite similar

  Hope this helps

  F. Javier B. · 1 · Aug 10 2018

• How do you plot a function on a cartesian plane?
• What does `(x,y)` mean?
• How do you plot `(1,-4)` on the coordinate plane?
• Where is the x-axis and y-axis located?
• What is the input and the output for the points `(2,3)` and `(-4, 0)`?
• How would you create a `(x,y)` table for the equation `y=2x-1`?
• Which quadrant does `(-3, 4)` lie in?
• How would you plot the point `(-4,0)` on the cartesian plane?
• How do you find the polynomial function whose graph passes through (2,4), (3,6), (5,10)?
• What are the asymptotes of (x^2+4)/(6x-5x^2)?
• What is an asymptote?
• Do asymptotes always converge to a value?
• What is the difference between a vertical and horizontal asymptote?
• Can a function have a vertical asymptote?
• What are the vertical and horizontal asymptotes of `y = (x+3)/(x^2-9)`?
• What are the vertical and horizontal asymptotes of `y = ((x-3)(x+3))/(x^2-9)`?
• What is the formula for the vertical asymptotes of tan(x)?
• What are the asymptotes of: `f(x)= (3e^(x))/(2-2e^(x))`?
• What are the asymptote(s) and hole(s) of: `f(x)=(x^2+x-12)/(x^2-4)`?
• What is the asymptote of: `f(x) = 1/x - x`?
• What are the horizontal and vertical asymptotes of: `f(x)=xtan(x)`?
• What are the asymptotes of `f(x)=(4tan(x))/(x^2-3-3x)`?
• What are the asymptotes of `f(x) = tan(2x)`?
• Does `f(x) = tan(2x)` have more asymptotes than `g(x)=tan(x)`?
• What are the asymptotes of `f(x) = (2x-1) / (x - 2)`?
• What are the asymptotes of `y=(2x^2 +1)/( 3x -2x^2)`?
• What is the difference between an asymptote and a hole?
• Does `f(x)=((x-1)(x+1))/(x^2-1)` have an asymptote or a hole?
• What are the asymptotes of `f(x)=(1/(x-10))+(1/(x-20))`?
• What are the asymptotes of `f(x)=(1-5x)/(1+2x)`?
• Is the following set of ordered pairs a function: (4,5),(3,4),(-2,5),(6,-8),(5,1)?
• Is (1,2), (2,2), (4,5), (1,-4) a function?
• Is (3,4),(5,1)(6,3),(6,4) a function?
• How do you decide whether the relation `y = - 7 / 2x - 5` defines a function?
• How do you decide whether the relation `y=x^6` defines a function?
• How do you decide whether the relation `2x + 4y = 5` defines a function?
• How do you decide whether the relation `x^2 + y = 81` defines a function?
• How do you decide whether the relation `x^2 + y^2 = 1` defines a function?
• How do you decide whether the relation `x + y^3 = 64` defines a function?
• How do you decide whether the relation `2x^2+7y^2=1` defines a function?
• How do you decide whether the relation `xy=9` defines a function?
• How do you decide whether the relation `sqrt(x+40)` defines a function?
• How do you decide whether the relation `abs(x)-y=5` defines a function?
• How do you decide whether the relation `x=y^2` defines a function?
• How do you decide whether the relation `f(x)= x/ [(x+2)(x-2)]` defines a function?
• How do you decide whether the relation `x + y = 25` defines a function?
• How do you decide whether the relation `x^2 + y^2 = 25` defines a function?
• How do you decide whether the relation `7x^2+y^2=1` defines a function?
• How do you decide whether the relation `xy+7y=7` defines a function?
• How do you decide whether the relation `(x-3)^2 + (y+1)^2 = 25` defines a function?
• How do you decide whether the relation `4x-7y=3` defines a function?
• How do you decide whether the relation `x^2-3y =12` defines a function?
• How do you decide whether the relation `x - 3y = 2` defines a function?
• How do you decide whether the relation `x = y^2 - 2y + 1` defines a function?
• How do you decide whether the relation `x^2 +y^2 =16` defines a function?
• How do you decide whether the relation `y = 13x+1` defines a function?
• How do you decide whether the relation `│2y│ = 4x` defines a function?
• How do you decide whether the relation `x = y²` defines a function?
• How do you decide whether the relation `3y - 1 = 7x +2` defines a function?
• How do you decide whether the relation `y^2 =4x` defines a function?
• Question #cc781
• Find all real functions f from `RR->RR` satisfying the relation `f(x²+yf(x))=xf(x+y)` ?
• Question #e4125
• Let `RR` denoted the set of real numbers. Find all functions `f:RR->RR`,satisfying `abs(f(x) - f(y)) = 2 abs(x-y)` for all `x,y` belongs to `RR`.?
• Question #6c402
• What is the difference between an axiom and a property?
• Question #f6f50
• How do you find the vertical, horizontal, and oblique asymptotes of `H(x)=(x^4+2x^2+1)/(x^2-x+1)`?
• Is that true to say: For every set A defined by A={ A : ∅∉A } then the Cardinality of A equals to |A|-1 ?
• Question #294f3
• Do the following equations define functions: (i) `y = x^2-5x` (ii) `x = y^2-5y` ?
• Question #0bb54
• Question #ced88