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  1. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

  2. Click the 'Go' button to instantly generate the derivative of the input function. The calculator provides detailed step-by-step solutions, facilitating a deeper understanding of the derivative process. implicit\:derivative\:\frac {dy} {dx},\: (x-y)^2=x+y-1.

  3. Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step.

  4. The point P (−2, −5) lies on the curve with equation y = f (x), x ∈ Find the point to which P is mapped, when the curve with equation y = f (x) is transformed to the curve with equation (a) y = f (x) + 2 (1) (b) y = | f (x) | (1)

  5. Example 1. Sketch the graph of g(x) = √x + 4. Solution: Begin with the basic function defined by f(x) = √x and shift the graph up 4 units. Answer: A horizontal translation is a rigid transformation that shifts a graph left or right relative to the original graph.

  6. The inverse function calculator finds the inverse of the given function. If f (x) f (x) is a given function, then the inverse of the function is calculated by interchanging the variables and expressing x as a function of y i.e. x = f (y) x = f (y).

  7. x y' (x) - 4 y (x) = x^6 exp (x), y (1) = 0. See the steps for using Laplace transforms to solve an ordinary differential equation (ODE): solve y' (t) - 3y (t) = delta (t - 2), where y (0) = 0.

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