#Sketching functions worksheet how to

Let us plot all the information on the graph.So let us take some random numbers on both sides of x = 0 and frame a table. We only have one data so far which is (0, 3). We do not have data about VA or x-intercept.

But it has a horizontal asymptote at y = 2.

Its domain is the set of all real numbers (R) and its range is y > 2.

We will graph it using the same steps as mentioned above.

Let us plot all these points along with VA and HA.Д¬onsider an exponential function f(x) = 2 -x + 2.

Let us take some random values on both sides of the vertical asymptote x = 2 and calculate the respective y-values.

Vertical asymptote (VA) is x = 2 and horizontal asymptote (VA) is y = 1.

Its x-intercept is (-1, 0) and y-intercept is (0, -0.5).

#Sketching functions worksheet how to

To understand how to find the domain and range of a rational function, click here. We follow the above steps and graph this function. Let us graph a rational function f(x) = (x + 1) / (x - 2). Let us see how to graph a function in different cases using the above steps.

Plot the points from the table, and join them by taking care of asymptotes, domain, and range.

Construct a table of values by taking some random numbers for x (on both sides of x-intercept and/or on both sides of the vertical asymptote), calculate the corresponding values of y.

Find the asymptotes ( vertical, horizontal, and slant) and draw them by dotted lines so that we can break the graph along those lines and make sure that the graph doesn't touch them.

Find x-intercept(s) and y-intercept(s), and plot them.

Find the domain and range of the function and keep it in mind while drawing the curve.

In each of these cases, for graphing functions, we follow the following steps: Just have an idea of how the graphs of parent functions of each of these functions look like.

Logarithmic Functions - Its parent function is of the form f(x) = log x.

Exponential functions - Its parent function is of the form f(x) = a x.

Rational functions - Its parent function is of the form f(x) = 1/x (which is called the reciprocal function).

There are some complex functions for which domain, range, asymptotes, and holes have to be taken care of while graphing them. But it is NOT the case with all types of functions. Graphing functions is comparably simple if each of their domain and range is the set of all real numbers. Now, we will plot the points (-1, 8), (0, 5), (1, 4), (2, 5), and (3, 8) on a graph sheet, join them, and extend the curve on both sides. Then we can calculate the y-coordinates using the function. We will take two random numbers on each side of 1 (which is the x-coordinate of the vertex) and frame a table. After finding the vertex, we can find two or three random points on each side of the vertex and they would help in graphing the function.Д®xample: Graph the quadratic function f(x) = x 2 - 2x + 5.Д¬omparing it with f(x) = ax 2 + bx + c, a = 1, b = -2, and c = 5. This is because, to get a perfect U-shaped curve, we need where the curve is turning. But this may not give a perfect U-shaped curve. Graphing Quadratic FunctionsДЇor graphing quadratic function also, we can find some random points on it.

If we plot them on a graph and join them by a straight line (extending the line on both sides), we get its graph as shown in the previous section. Thus, two points on the line are (0, 2) and (1, 1). Then substitute each of these in y = -x + 2 to compute y-values. For this, we create a table of values by taking some random numbers for x say x = 0 and x = 1. Let us graph the same linear function as mentioned in the previous section (f(x) = -x + 2).

finding some points on it, by substituting some random values of x and finding the corresponding values of y by substituting each value into the function.

For example, if it is a linear function of the form f(x) = ax + b, then its graph would be a line if it is a quadratic function of the form f(x) = ax 2 + bx + c, then its a parabola. Graphing basic functions like linear functions and quadratic functions is easy.