Free online graphing calculator for math functions 2d

Linear function y=f(x)=ax+b represent always straight line and can be sketch by joining only two points . As for example y=f(x)=2x+1 is a linear function which can be draw by joining two points (1,3) and (3,7). Free graphing calculator for math drawing website www.graph2d.com can draw any linear function. You can type 2*x+1 in the input box and then the graph will drawn automatically. You can also try to draw with the function f(x)=x, f(x)=3x+1, f(x)=-2x+3, f(x)=-x-5, f(x)=5x-1 etc. For learn about piecewise functions of Mathematics and graphing, visit: Graphing piecewise function of Math.

A polynomial function of degree one or zero is called linear function. The graph of linear function is always represent a straight line which can be drawn by graph of linear function clculator,browsing link: Graphing calculator of Math

Quadratic function y=f(x)=ax²+bx+c always represent a parabola. If the co-efficient of x² is positive , the parabola will be concave up and negative , the parabola will be concave down. For manually sketch the quadratic function graph, we will find two points for which y=f(x)=0 that means the parabola passes through this two points and the concavity of parabola depend on the co-efficient of x² . As for example y=f(x)=x²-5x+4=(x-1)(x-4). If x=1 or x=4, then y will be zero.That means the parabola passes through (1, 0) and (4, 0). Since the co-efficient of x² is 1 which is positive, so the parabola will be concave up. Geogebra Free graphing calculator for math graph drawing website www.graph2d.com can draw any qudratic function. You can type x**2-5*x+4 in the input box and then press drawing button to get the graph. You can also try to draw with the function f(x)=x², f(x)=-x², f(x)=x²+5x, f(x)=x²-3x, f(x)=x²+2x+5 etc.

If we find only one point for which y=0, then the parabola touches x-axis on that point. As for example, y=f(x)=2(x-2) ², there is only one point (2, 0) for which y=0, so the parabola touches x-axis at (2, 0) which is critical point. Since the co-efficient of x² is 2 which is positive, so the parabola will be concave up. Free graphing calculator for math drawing website www.graph2d.com can draw any qudratic function. You can type 2*(x-2)**2 in the input box and then the graph will drawn automatically.

If we can not find any point for which y=0, then we will try to get a term of whole square. As for example, y=f(x)=x²-4x+7=(x-2) ²+3. When x=2, then the (x-2) ²=0 and hence y=3. So the point (2, 3) is a critical point. Since the co-efficient of x² is 1 which is positive, so the parabola will be concave up. Free graphing calculator for math drawing website www.graph2d.com can draw any qudratic function. You can type x**2-4*x+7 in the input box and then the graph will drawn automatically. For learn about Implicit function of Mathematics and graphing, visit: Graphing Implicit function of Math.

A polynomial function of degree two is called quadratic function. The graph of quadratic function is always represent a parabola which can be drawn by quadratic function graph maker,browsing link: Graphing calculator of Math

Cubic function y=f(x)=ax³+bx²+cx+d represent a curve. At first we find the value of x for which y=0. If the number of same roots of y=0 is odd number, then that point the graph will crosses on x-axis and is even number , then the graph will touches on thex-axis. If the co-efficient of x³ is positive, then the curve will sketch from upper side of x-axis of right side and is negative, then the curve will sketch from lower side of x-axis of right side. As for example, y=f(x)=(x-3) ²(x-7),there are two(even number) same roots x=3 and one(odd number) root x=7 .So the curve touches at x=3 with x-axis and crosses at x=7 with x-axis. Since the co-efficient of x³ is 1 which is positive, so the curve will sketch from upper side of x-axis of right side. .Free online graphing calculator for math for graph drawing website www.graph2d.com can draw any cubic function. You can type (x-3)**2*(x-7) in the input box and then the graph will drawn automatically. You can also try to draw with the function f(x)=x³, f(x)=-x³, f(x)=x³ -4x², etc. For learn about Calculator of Mathematics and graphing, visit: Graphing Calculator of Math.

A polynomial function of degree three is called cubic function. The graph of cubic function is always represent a continous curve which has maximum two turning point.. The graph of cubic function can be drawn by Graphing calculator of Math

Rational function y=f(x)=P(x)/Q(x) is a ratio of two polynomials P(x) and Q(x). As for example, y=f(x)=(x²+1)/x=x+1/x is a rational function. There are two asymptotes y=x and x=0.The graph of this rational function is two curves which are situated between this two asymptotes. Free online graphing calculator for math for graph drawing website www.graph2d.com can draw any rational function. You can type (x**2+1)/x in the input box and then the graph will drawn automatically. You can also try to draw with the function f(x)=x-1/x , f(x)=(x+1)/x , f(x)=1/x, f(x)=(x+1)(x+3)/(x-2) etc. For learn about complex analysis of Mathematics and graphing, visit: Graphing Complex analysis of Math.

Trigonometric function is a ratios of two side lengths of of a right-angled triangle. It is also called circular function. Free online graphing calculator for math for graph drawing website www.graph2d.com can draw any trigonometric function. You can type Math.sin(x) in the input box and then the graph will drawn automatically of sin(x).You can also change x-scale and y-scale. You can also try to draw with the function f(x)=cos(x), f(x)=tan(x), f(x)=cos(2x), f(x)=sin(2x), f(x)=tan(2x) etc. For learn about Linear Programming or Operation research of Mathematics and graphing, visit: Graphing Linear programming or operation research of Math.

Inverse circular function is a arcus or inverse trigonometric or antitrigonometric function. Free online graphing calculator for math for graph drawing website www.graph2d.com can draw any antitrigonometric function or inverse circular function. You can type Math.asin(x) in the input box and then the graph will drawn automatically of sin^-1(x).You can also change x-scale and y-scale. You can also try to draw with the function f(x)=cos^-1(x), f(x)=tan^-1(x), f(x)=sin^-1(2x) etc. For learn about Inequality of Mathematics and graphing, visit: Graphing Inequality of Math.

Exponential function is a function which is denoted by f(x)=a^x=e^xlna or f(x)= e^x where the mathematical constant e =1+(1/1!)+(1/2!)+(1/3!)+... ...to ∞ and the value of e is approximately 2.718. Free online graphing calculator for math for graph drawing website www.graph2d.com can draw any exponential function function. You can type Math.exp(x) in the input box and then the graph will drawn automatically of e^x.You can also change x-scale and y-scale. You can also try to draw with the function f(x)=e^-x, f(x)=e^-2x, f(x)=e^-3x, f(x)=e^2x, f(x)=e^3x, f(x)=10^x, f(x)=10^-x,f(x)=5^x etc. For learn about Polar function of Mathematics and graphing, visit: Graphing Polar function of Math.

Logarithmic function is a function which is denoted by f(x)=log(x) or f(x)= ln(x). Free online graphing calculator for math for graph drawing website www.graph2d.com can draw any logarithmic function. You can type log(x) in the input box and then the graph will drawn automatically of log(x).You can also change x-scale and y-scale. You can also try to draw with the function f(x)=log(2x), f(x)=log(3x-5), f(x)=5log(1-x), f(x)=ln(x), f(x)=ln(5x-2), f(x)=3ln(2x-1), f(x)=2+ln(x),f(x)=2-log(x) etc. For learn about Parametric function of Mathematics and graphing, visit: Graphing Parametric function of Math.

In Mathematics, The transcendental function is a function which is combination of Exponential function, logarithmic function, Trigonometric function, Inverse circular function etc i.e. transcendental function is not an algebriac function. As for example, sin(2x), tan(x), log(x), log(3x), ln(2x), sin^-1(x), cot^-1(x), e^x, e^-2x etc are transcendental functions. We can draw any graph of transcendental function with the free graph drawing website www.graph2d.com. As for example, the graph of f(x)=e^x+sin(2x) is drawing by www.graph2d.com. For drawing type e^x+sin(2x) in the input box and then the graph will drawn automatically. The graph of that function is given belows. For learn about Parallilogram law on Mechanics of Mathematics and graphing, visit: Graphing Parallilogram law on mechanics of Math.

In Mathematics, The odd function f(x) is a function which is satisty f(-x)=-f(x). As for example, sin(x), tan(x), x³, x⁷ etc are odd functions.The odd functions are symmetric about origin. We can draw any graph of odd function with the free graph drawing website www.graph2d.com. As for example, the graph of f(x)=x³. For drawing type x^3 in the input box and then the graph will drawn automatically of the odd function f(x)=x³. The graph of that function is given belows. For learn about Simple Calculator of Mathematics and graphing, visit: Simple Calculator of Math.

In Mathematics, The even function f(x) is a function which is satisty f(-x)=f(x). As for example, cos(x), x², x⁴ etc are even functions.The even functions are symmetric about y-axis. We can draw any graph of even function with the free graph drawing website www.graph2d.com. As for example, the graph of f(x)=x⁴-x². For drawing type x^4-x^2 in the input box and then the graph will drawn automatically of the even function f(x)=x⁴-x². The graph of that function is given belows. For learn about Piecewise function of Math and graphing, visit: Graphing piecewise function of Mathematics.

In Mathematics, The hyperbolic function are similar to see the Trigonometric function or Circular function .The hyperbolic function are defined the combination of Exponential function e^x and e^-x. As for example, sinh(x)=(e^x-e^-x)/2, cosh(x)=(e^x+e^-x)/2, tanh(x)=(e^x-e^-x)/(e^x+e^-x),cosech(x)=2/(e^x-e^-x), sech(x)=2/(e^x+e^-x), coth(x)=(e^x-e^-x)/(e^x+e^-x). We can draw any graph of hyperbolic function with the free graph drawing website www.graph2d.com. As for example, the graph of f(x)=coth(x). For drawing type coth(x) in the input box and tthen the graph will drawn automatically the graph of the hyperbolic function f(x)=coth(x). The graph of that function is given belows. For learn about Implicit function of Mathematics and graphing, visit: Graphing Implicit function of Math.

In Mathematics, The constant function is a function whose range is a single element on whole domain. As for example, f(x)=5, f(x)=e, f(x)=π etc are constant functions . We can draw any graph of constant function with the free graph drawing website www.graph2d.com. As for example, the graph of f(x)=7. For drawing type 7 in the input box and then the graph will drawn automatically of the constant function f(x)=7. The graph of that function is given belows. For learn about Complex analysis of Mathematics and graphing, visit: Graphing Complex analysis of Math.

In Mathematics, The square root of a function is defined as f(x)=√(h(x)) where h(x) is another function. We can draw any 2d graph of square root function with the free graph drawing website www.graph2d.com. As for example, the graph of f(x)=√(2x+5). For drawing type sqrt(2x+5) in the input box and then the graph will drawn automatically of the square root function f(x)=√(2x+5). The graph of that function is given bellows. For learn about Linear programming of Mathematics and graphing, visit: Graphing linear programming of Math.

The graph drawing website www.graph2d.com can draw any graph in 2D of mixed function of algebriac function and trigonometric function. As for example, the graph of f(x)=xsin²x. For drawing type xsin(x)^2 in the input box and tthen the graph will drawn automatically of mixed function f(x)=xsin²x. The graph of that function is given belows. For learn about Inequality of Mathematics and graphing, visit: Graphing Inequality of Math.

The domain of a function y=f(x) is the set of all possible values of independent variable x and the range of a function y=f(x) is the set of all possible values of dependent variable y. The domain is denoted by Domf and the range is denoted by Rangf. From the graph of a function, we can determine the domain and range. As for example, y=f(x)=√(x+5). The graph is situated from -5 to ∞ on the horizontally . So Domf=(-5, ∞). Again the graph is situated from 0 to ∞ on the vertically . So Rangf=(0, ∞) For learn about Polar function of Mathematics and graphing, visit: Graphing Polar function of Math.

Ceiling function : The Ceiling function is a special type of function which has returns the smallest integer value which is greater than or equal to the specified number. The Ceiling function is denoted by f(x)=⌈x⌉. As for example, f(3.4)=⌈3.4⌉=4. The graph of ceiling function is given belows.

Floor function : The Floor function is a special type of function which has returns the largest integer value which is less than or equal to the specified number. The Floor function is denoted by f(x)=⌋x⌊ As for example, f(3.4)=⌋3.5⌊=3. The graph of floor function is given belows.

A Linear cost function is used in Business to find out the total cost which is relation between total cost and total amount of production units. The linear cost function is denoted by f(x)=mx+c where f(x) is total cost, mx is variable cost, c is fixed cost, x is total production units and m is variable cost per unit production. As for example, A small ball pen factory has fixed cost $100, variable cost per pen is $5, then the cost function will be f(x)=5x+100. If this factory make 100 pcs ball pen, then variable cost=$5X100=$500 and fixed cost=$100, so total cost=$500+$100=$600 but if we use the cost function, we get f(100)=5X100+100=600.Again if thisball pen factory make 20 pcs ball pen, then total cost f(20)=5X20+100=200.

suppose that a hostel has 5 members and total cost $250. If the hostel has 7 members, then the total cost $330. Now we make a linear relationship between number of hostel members and the total cost for finding the linear cost function. let (x1,y1)=(5, 250) and (x2,y2)=(7, 330). We know that the linear relationship is (x-x1)/(x1-x2)=(y-y1)/(y1-y2) ⇒ (x-5)/(5-7)=(y-250)/(250-330) ⇒(x-5)/(-2)=(y-250)/(-80) ⇒(x-5)/1=(y-250)/40 ⇒ y-250=40x-200 ⇒ y=40x-200+250 ⇒ y=40x+50. So the linear cost function for the hostel members is f(x)=40x+50 where the fixed cost is $50, variable cost per member is $40, variable cost for all members is $40x and the total cost=variable cost+fixed cost i.e. f(x)=40x+50. If the number of hostel members is 10, then the total cost be f(10)=40X10+50=450 dolars.

If we draw graph of any function and its inverse function in same graph paper, then we see that the both graph are symmetric about the straight line y=x. Let us consider a rational function f(x)=(2x-1)/(x+1). Now we find the inverse function of this rational function. For finding the inverse function, substituting x by f^-1(x) in this rational function, we get, f(f^-1(x))=(2f^-1(x)-1)/(f^-1(x)+1) ⇒x=(2f^-1(x)-1)/(f^-1(x)+1) ⇒xf^-1(x)+x=2f^-1(x)-1 ⇒ xf^-1(x)-2f^-1(x)=-x-1 ⇒ f^-1(x)(x-2)=-x-1 ⇒ f^-1(x)=(-x-1)/(x-2) ⇒ f^-1(x)=(x+1)/(2-x) Now we drawing the graph of this rational function and its inverse function in the same graph paper with free graphing calculator, then we get the graph of function f(x) with red color and the inverse function f^-1(x) with blue color. We oserve that the both graphs(red curve and blue curve) are symmmetric about the straight line y=x with black color line. This observation(symmetric graph of any function and its inverse function about the straight line y=x ) are applicable for any function and its inverse function which is the relation between any function and its inverse function.

A function y=f(x) has an asymptote if the distance between a straight line and the curve of this function tends to zero when the points on the curve approach to infinity. As for example the function y=f(x)=1/x has two asymptotes x-axis (y=0) and y-axis (x=0) because the distance between x-axis or y-axis and the curve tends to zero when the points on the curve approach to infinity.

The domain of a polynomial function is set of real number except the abscissa of vertical asymptotes and The range of a polynomial function is the set of images which does not contain the ordinate of the horizontal asymptotes. From the above example, domain=R-{0} and the range =R-{0} because the ordinate of vertical asymptote is 0 and the ordinate of the horizontal asymptote is 0.

The concavity of a function is identify by its second derivatie. if the second derivative of the function is positive on a interval, then the function is concave up on this interval and if the second derivative is negative on a interval, then the function is concave down on the interval. As for example, f(x)=x³-3x²+4 and its first derivatives f'(x)=3x³-6x and second f''(x)=6x-6. If f''(x)>0 or 6x-6>0 or x>1, then the function is concave up on the interval (1, ∞). Again If f''(x) <0 or 6x-6<0 or x<1, then the function is concave down on the interval (-∞, 1). You can also solve the inequality by the graphical method with graphing of inequality. The graph of the function f(x) and its concavity is given belows.

If f'(x) is greater than zero on an interval, then function f(x) is increasing on that interval and if f'(x) is less than zero on an interval, then function f(x) is decreasing on that interval. As for example, f(x)=x²-6x and its first derivatives f'(x)=2x-6. If f'(x)>0 or 2x-6>0 or 2x>6 or x>3, then the function is increasing on the interval (3, ∞). Again If f'(x) <0 or 2x-6<0 or x<3, then the function is decreasing on the interval (-∞,3). You can also solve the inequality by the graphical method with graphing of inequality. The graph of the function f(x) and increasing and decreasing interval is given belows.