**McCall Faciszewski**

Pre-Calculus H 3A

Pre-Calculus H 3A

**Sections 2.6, 2.7, & 2.8**

2.6 Graphs of Rational Functions

Rational Function- The domain of a rational function is the set of all real numbers except the zeros of its denominator.

End Behavior Asymptote- The values that indicate what the end behavior of a function is approaching and looks like on a graph.

Vertical Asymptote- These occur at the real zeros of the denominator, provided that the zeros are not also zeros of the numerator of equal or greater multiplicity.

X-intercepts-These occur at the real zeros of the numerator, which are not also zeros of the denominator.

Y-intercept- This is the value of f(0), if defined.

Slant Asymptote- The end behavior of an asymptote of a rational function is a slant line.

Vocabulary

2.6 Graphs of Rational Functions

http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-algebra/19-graphing-rational-functions-01.htm

http://www.themathpage.com/aprecalc/rational-functions.htm

http://www.brightstorm.com/math/precalculus/polynomial-and-rational-functions/

https://www.khanacademy.org/math/algebra2/rational-expressions/rational-function-graphing/e/graphs-of-rational-functions

Helpful Websites

2.6 Graphs of Rational Functions

The skills in this section are used when exploring relative humidity. The inverse proportion of constant vapor pressure to saturated vapor pressure is used to determine the relative humidity in various conditions. Daily weather reports use the graphs of the rational function of humidity in order to predict, analyze, and report it.

Principles in Chemistry, such as Boyle's Law, use the techniques in this section to analyze how temperature and volume are related. The comparison of power and rational functions are used to find the relationship between two measurements, and then often used to find an unknown in chemistry.

Real World Applications

2.6 Graphs of Rational

Functions

**Helpful Videos**

2.7 Solving Equations in One Variable

Rational Equations- Equations involving rational expressions or fractions

Extraneous Solutions- Solutions that are not solutions of the original equation and do not work in it.

2.8 Solving Inequalities in One Variable

No Vocabulary

2.7 Solving Equations in One Variable

http://www.purplemath.com/modules/solvelin.htm

https://www.bulbapp.com/u/precalculus-2-6-2-7-rational-function-graphs-and-solving-equations

http://college.cengage.com/mathematics/blackboard/shared/content/interactive_lessons/0072/toc.html

http://www.slideshare.net/JarrettM81/clearing-fractions

2.8 Solving Inequalities in One Variable

http://www.algebra-class.com/solving-inequalities.html

http://www.montereyinstitute.org/courses/Algebra1/COURSE_TEXT_RESOURCE/U05_L1_T1_text_final.html

http://www.mathplanet.com/education/algebra-1/linear-inequalitites/solving-linear-inequalities

http://www.regentsprep.org/regents/math/algebra/AE8/LSolvIn.htm

2.7 Solving Equations in One Variable

Chemists use one variable equations like in this section to calculate exactly what proportion of acid and solution must be mixed together to make the correct dilution.

One variable equations can also be used in the real world to solve for the minimum perimeter of a rectangle. Someone like a land surveyor or an architect could use this technique if they know the area of a rectangle and need the perimeter.

2.8 Solving Inequalities in One Variable

Package designing companies use inequalities to determine exactly how large or small a measurement need to be, depending on the desired volume or specified dimension. They can set up exact inequalities using their initial desired values and solve for the unknown.

Inequalities are also useful when companies are determining their budget. Inequalities can be set up based upon the set budget and the different levels of funding, such as employee salaries, can be determined.

2.7 Solving Equations with One Variable

2.8 Solving Inequalities with One Variable