Graph of the function is given below
Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, needs some skill and some mathematical concepts to understand
Graphing functions is drawing the curve that represents the function on the coordinate plane. If a curve (graph) represents a function, then every point on the curve satisfies the function equation.
For example, the following graph represents the linear function f(x) = -x+ 2.
Take any point on this line, say, (-1, 3). Let us substitute (-1, 3) = (x, y) (i.e., x = -1 and y = 3) in the function f(x) = -x + 2 (note that it can be written as y = -x + 2). Then
3 = -(-1) + 2
3 = 1 + 2
3 = 3, thus, (-1, 3) satisfies the function.
In the same way, you can try taking different points and checking whether they satisfy the function. Each and every point on the line (in general called "curve") satisfies the function. Drawing such curves representing the functions is known as graphing functions
Graphing functions is comparably simple if each of their domain and range is the set of all real numbers. But it is NOT the case with all types of functions. There are some complex functions for which domain, range, asymptotes, and holes have to be taken care of while graphing them. The most popular such functions are:
Rational functions - Its parent function is of the form f(x) = 1/x (which is called the reciprocal function).
Exponential functions - Its parent function is of the form f(x) = ax.
Logarithmic Functions - Its parent function is of the form f(x) = log x.
Let us graph a rational function f(x) = (x + 1) / (x - 2). We follow the above steps and graph this function.
Domain = {x ∈ R | x ≠ 2} ; Range = {y ∈ R | y ≠ 1}. To understand how to find the domain and range of a rational function, click here.
Its x-intercept is (-1, 0) and y-intercept is (0, -0.5).
There are no holes.
Vertical asymptote (VA) is x = 2 and horizontal asymptote (VA) is y = 1.
Let us take some random values on both sides of the vertical asymptote x = 2 and calculate the respective y-values.
learn more about graph of function here : brainly.com/question/9834848
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