datesrefa.blogg.se - Function graph

#FUNCTION GRAPH HOW TO#

a - The division of f(x) by x - 2 gives a quotient equal to -x 2 - 2x -1 and a remainder is equal to 0.

Show that x - 2 is a factor of f(x) and factor f(x) completely.

Adding to all these properties the left and right hand behaviour of the graph of f, we have the following graph. The graph cuts the x axis at x = -2, -1 and 1. The y intercept of the graph of f is at (0, - 2).

d - The leading coefficient f(x) is positive, the graph of f is down on the left and up on the right and hence the range of f is the set of all real numbers.

Therefore the graph of f cuts the x axis at all these x intercepts.Ĭ - The domain of f (x) is the set of all real numbers.

Function f has zeros at x = - 2, at x = 1 and x = - 1.

Adding to all these properties the left and right hand behavior of the graph of f, we have the follwoing graph.

Is that of f(x) = x 3 shifted 2 units to the right because of the term (x - 2) and reflected on the x axis because of the negative sign in f(x) = - (x - 2) 3. The y intercept is a point on the graph of f. After expansion of f(x), we can see that the leading coefficient (of x 3) is negative, the graph of f is down on the right and up on the left and hence the range of f is the set of all real numbers.Īt x = 2, the graph cuts the x axis.c - The domain of f (x) is the set of all real numbers.Function f has one zero at x = 2 of multiplicity 3 and therefore the graph of f cuts the x axis at x = 2.Use the y intercept, x intercepts and other properties of the graph of to sketch the graph of f.Find all zeros of f and their multiplicity.Since the leading coefficient (of x 3) is positive, the graph of f is up on the right and down on the left and hence the range of f is the set of all real numbers.Īlso since f(-x) = - f(x), function f is odd and its graph is symmetric with respect to the origin (0,0).b - The domain of f (x) is the set of all real numbers.The x intercept are at the points (0, 0).The x coordinates of the x intercepts are the solutions to.Find the x and y intercepts of the graph of f.

If the leading coefficient is negative, as x increases f(x) decreases the graph of f is down and as x decreases indefinitely f(x) increases the graph of f is up. If the leading coefficient a is positive, as x increases f(x) increases and the graph of f is up and as x decreases indefinitely f(x) decreases and the graph of f is down. The left hand side behaviour of the graph of the cubic function is as follows: The x intercepts are found by solving the equation The y intercept of the graph of f is given by y = f(0) = d. The range of f is the set of all real numbers. The domain of this function is the set of all real numbers. Where a, b, c and d are real numbers and a is not equal to 0. Properties, of these functions, such as domain, range, x and y intercepts, zeros and factorization are used to graph this type of functions.

#FUNCTION GRAPH HOW TO#

A step by step tutorial on how to determine the properties of the graph of cubic functions and graph them.