![]() Reciprocal of a Fraction:: Reciprocal of a fraction can be obtained by flipping the places of numerator and denominator. ![]() Examples are, Reciprocal of x/(x - 4) is (x - 4)/x. Reciprocal of an Expression: The reciprocal of an expression can be found by exchanging the positions of numerator and denominator.Reciprocal of a Variable: The reciprocal of a variable 'y' can be found by dividing the variable by 1.Reciprocal of a Number: To find the reciprocal we divide the number, variable, or expression by 1.The method to solve some of the important reciprocal functions is as follows. As an exercise find the domains of the above functions and compare with the domains found graphically above.The reciprocal functions of some of the numbers, variables, expressions, fractions can be obtained by simply reversing the numerator with the denominator.Use the graph of f to determine its domain and range. Enter 1 / (x^2 - 1) in the editing window (which means f(x) = 1 / (x^2 - 1)).Enter sqrt(-x + 1) in the editing window (which means f(x) = sqrt(-x + 1).Enter -2sin(x) in the editing window (which means f(x) = -2sin(x)).Enter sqrt(x^2-9) in the editing window (which means f(x) = sqrt(x^2 - 9), sqrt means square root).Verify graphically that the domain of f is given by the interval. Enter sqrt(4 - x^2) in the editing window (which means f(x) = sqrt(4 - x^2), sqrt means square root).Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical testsģ - Determine Domain and Range of a Function From Graph Enter x^3+abs(x) in the editing window (which means f(x) = x^3+abs(x)).Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests. Enter x^3+1/x in the editing window (which means f(x) = x^3+1/x).Enter x^3 in the editing window (which means f(x) = x^3).Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests for even: f(x) = f(-x) and for odd: f(x) = - f(-x). Enter x^2 + abs(x) in the editing window (which means f(x) = x^2 + abs(x), abs means absolute value).Enter abs(x) in the editing window (which means f(x) = abs(x), abs means absolute value). ![]() Solve the equation x^2 - 2 x - 3 = 0 and find f(0) and compare to the x and y intercepts determined graphically. ![]() The x intercepts are found by solving x^2 - 2 x - 3 = 0 and the y intercept is given by f(0). Determine the y intercept (this is the point of intersection of the graph with the y axis). Determine (approximately) the x intercepts of the graphs (these are the points of intersection of the graph with the x axis). Enter x^2-2 x - 3 in the editing "f(x)" window (which means f(x) = x^2 - 2 x - 3) of the graphing calculator above.x - intercept is the solution to f(x) = 0 and the y-interecept is given by f(0). Enter function 2 x - 4 in editing "f(x)" window (which means f(x) = 2 x - 4) of the graphing calculator above and find the x and y intercepts graphically and check the answer by calculation.Interactive Tutorial 1 - x and y intercepts of graphs Zoooming is also available at the top right hand side of the graph and you may also download png files with the graph in it.Įxamples of expression for functions that may be entered. You may hover the mousse cursor to read coordinates of any point on the graph. Special constants e and pi are used as they are, leaving a space any of the constants and another constant or variable. Log(x), logarithmic function to the base eĪnd Square Root Functions Absolute Value and Log(x,a), logarithmic function base to the base a All the functions listed below are accepted by this calculator and they may be copied and pasted on the "f(x)" input window above if needed. ![]()
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