What are the steps to graphing a rational function?

What are the steps to graphing a rational function?

Process for Graphing a Rational Function

1. Find the intercepts, if there are any.
2. Find the vertical asymptotes by setting the denominator equal to zero and solving.
3. Find the horizontal asymptote, if it exists, using the fact above.
4. The vertical asymptotes will divide the number line into regions.
5. Sketch the graph.

What are the steps to solve a rational function?

The steps to solve a rational equation are:

1. Find the common denominator.
2. Multiply everything by the common denominator.
3. Simplify.
4. Check the answer(s) to make sure there isn’t an extraneous solution.

What is the third step in sketching the graph of a rational function?

Choosing test numbers to the left and right of each of the function’s zeros and finding the value of the function at each test number.

What are graphs of rational functions?

Rational functions are of the form y=f(x) , where f(x) is a rational expression . The graphs of the rational functions can be difficult to draw. To sketch a graph of a rational function, you can start by finding the asymptotes and intercepts.

What is the first step in sketching the graph of a rational function apex?

Place the steps to sketch the graph of a rational function in the appropriate order.

1. Find the function’s zeros and vertical asymptotes, and plot them on a number line.
2. Choose test numbers to the left and right of each of these places, and find the value of the function at the test number.

What are the types of function graphs?

Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.

What are the steps to graph rational functions?

Steps To Graph Rational Functions. Steps To Graph Rational Functions. 1. Make sure the numerator and denominator of the function are arranged in descending order of power. 2. Find the domain a. Factor the denominator of the function, completely. b. Find the real zeros of the denominator by setting the factors equal to zero and solving.

How to graph a rational function with asymptotes?

To graph a rational function of the form y= a x−h +k, follow these steps: Step 1Draw the asymptotes x=hand y=k. Step 2Plot points to the left and to the right of the vertical asymptote. Step 3Draw the two branches of the hyperbola so that they pass through the plotted points and approach the asymptotes. x y y= +k a x−h y=k x=h x y −4 2 2 −2

What is an example of a rational function?

Rational functions are of the form y = f x, where f x is a rational expression. Some of the examples of rational functions are: y = 1 x, y = x x 2 − 1, y = 3 x 4 + 2 x + 5 The graphs of the rational functions can be difficult to draw.

What does rewriting a rational function reveal?

Rewriting a rational function may reveal properties of the function and its graph. For example, rewriting a rational function in the form y= a x−h +kreveals that it is a translation of y= a — with vertical asymptote x x=hand horizontal asymptote y=k. Rewriting and Graphing a Rational Function Rewrite g(x) = 3x+ 5 x+ 1 in the form g(x) =