If f(x) represents a rational expression, then y = f(x) is a rational function. To graph a rational function, first find values for which the function is undefined. A function is undefined for any values that would make any denominator become zero. Dashed lines are drawn on the graph ...
• Simplify the rational function if possible. If any factors divide, remember them for “holes”. Y-intercept • Find and plot the y-intercept (if any) by evaluating f(0). X-intercept(s) • Find the zeros of the numerator (if any) by solving the equation N(x)=0. Then plot...
Steps to Graph a Rational Function • 1. Factor and simplify if you can • 2. Look for the vertical asymptote and horizontal asymptote • 3. Draw asymptotes as dotted lines on your graph • 5. Find 3 x values greater than the vertical asymptote and 3 less than the vertical asympto...
Graph the rational function given below. f(x) = (x2- x - 2) / (x - 2) Solution : Step 1 : First, we have to find hole, if any. To find hole of the rational function, we have to see whether there is any common factor found at both numerator and denominator. So, let us f...
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We learned that a rational function is the fraction of two polynomial functions and that a linear polynomial is a polynomial whose highest degree is 1. We learned that a shortcut for identifying rational functions with linear polynomials is to just look for an x with no exponent in both the...
To graph a rational function:Factor the numerator and denominator, if possible; check if anything can be cancelled out. Solve the numerator's factors for their zeroes; these will be the x-intercepts of the graph. Solve the denominator's factors for their zeroes, keeping in mind that the ...
x)increasesordecreaseswithoutboundasxapproachesa.f(x)-asxa+ yy f(x)-asxa- x=aaxfa x=ax f Thus,f(x)orf(x)-asxapproachesafromeithertheleftortheright.LocatingVerticalAsymptotes If p(x)f(x)=q(x)isarationalfunctioninwhich ...
Graph the function {eq}f(x)=\frac{x^{2} +x +2}{x^{2} -3x-4} {/eq}. 2. Identify which of the following graphs represents the rational function of {eq}f(x)=\frac{x^{2} +x-4 }{x^{2} +5x+6} {/eq}. 3. Plot the function of {eq}f(x)=\frac{x^{2} -...
An Example of Graphing a Rational FunctionIntroAn ExampleAnother ExampleThe Case with the HolePurplemath When you're graphing rational functions, take the time to label your asymptotes and intercepts. Plot enough points for you to feel confident in how the graphed line goes; plot more where you...