Functions on a Cartesian Plane
Understanding functions on a Cartesian plane is fundamental to grasping mathematical relationships within a two-dimensional space. The Cartesian coordinate system, devised by René Descartes, provides a framework for plotting points and exploring the behavior of functions. In this context, a function assigns a unique output value to each input, mapping a precise correspondence between the elements of the domain and range. Through this lens, we gain insights into patterns, symmetry, and the broader interplay between variables. Functions on a Cartesian plane serve as a cornerstone in mathematical analysis, facilitating the interpretation of real-world phenomena and underpinning various mathematical disciplines.
Questions
- How do you decide whether the relation # x^2 + y = 81# defines a function?
- Do the following equations define functions: (i) #y = x^2-5x# (ii) #x = y^2-5y# ?
- Is the following set of ordered pairs a function: (4,5),(3,4),(-2,5),(6,-8),(5,1)?
- How do you decide whether the relation #x + y^3 = 64# defines a function?
- What is the input and the output for the points #(2,3)# and #(-4, 0)#?
- How do you decide whether the relation #y = 13x+1# defines a function?
- Find all real functions f from #RR->RR# satisfying the relation #f(x²+yf(x))=xf(x+y)# ?
- What are the asymptotes of #y=(2x^2 +1)/( 3x -2x^2)#?
- How do you decide whether the relation #x^2 + y^2 = 1# defines a function?
- How do you decide whether the relation #sqrt(x+40)# defines a function?
- What are the vertical and horizontal asymptotes of #y = (x+3)/(x^2-9)#?
- X€[-1;0] and -2y€[-2;2] then #(x-2y)^2#€...?
- What is the formula for the vertical asymptotes of tan(x)?
- How do you decide whether the relation #x + y = 25# defines a function?
- Find two functions f and g such that h(x) can be expressed as the function indicated. h(x) = 4x + x2; f − g?
- Which quadrant does #(-3, 4)# lie in?
- How do you decide whether the relation #abs(x)-y=5# 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 #y=x^6 # defines a function?
- Find the values of x and y? x+4iy=ix+y+3