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Algebra II-Chapter 9
Rational Functions
| Question | Answer |
|---|---|
| In graphing, what is a branch? | Disting part of a curve |
| What axis if the horizontal asymptote? | X-axis |
| What asix is the vertical asymptote | Y-axis |
| Direct variation | whenn x varies directly with y and vice-versa. Linear function of the form y=kx, where k is nonzero constant |
| Inverse variation | as x increases, y decreases or vice-versa. Function of the form y = k/x or xy =k, where k is not 0 |
| What is the inverse variation model (equation) | y = k/x |
| How do you write the function that models an inverse variation? | 1. must have value for x and value for y2. write the model equation (y=k/x)3. substitute the values for x and y4. find k5. use the value of k to write the function |
| What is relationship if x increases and y increases the same amount? | Direct varation |
| What is the relationship if x increases and y decreases by the same amount? | Inverse variation |
| What is the relationship if x increases and y decreases but by different amounts | No relationship |
| Combined variation | combines direct and inverse variations in more complicated relationships |
| In the following equation what is the relationship of x and y to z (z = kx/wy)? | 1. z varies directly with x2. z varies inversely with the producty of y (and also w) |
| when k is positive, where are the branches of y = k/x (Quadrant) | Quadrant I and III |
| when k is negative, where are the branches of y - k/x (Quadrant) | Quadrant II and IV |
| In an equation y = 4/x-2, what is the vertical asymptote? | x - 2 is the vertical asymptote |
| What is the vertical asymptote for y = 4/x | x = 0 is the vetical asymptote |
| Translate the following inverse variation into its properties y = k/(x-b)+c | b= horizontal unit (x = b which is the vertical asymptote)c= vertical unit (y = c or the horizontal asymptote) |
| How do you write the equation of a translation? | 1. first write the first equation2. must know the asymptotes3. write the general form of a translation4. substitute the asymptotes values provided5. simplify |
| What is the general form of an translation? | y = k/(x-b)+c |
| T or F: Is an inverse variation an example of a rational function? | True |
| How do you write a rational function? | f(x) = P(x) /Q(x); where P and Q are polynomial functions and Q(x) cannot equal 0 |
| What is a rational function | A ratio of functions |
| What is continuous graph of a rational function? | No value in the denominator that makes x= 0 (no value of x that makes the denominator 0) |
| What is a discontinuous graph of a rational function? | a value that makes x = 0 |
| KEY POINT**** the domain of f cannot be a number that causes the denominator to be zero!!! | KEY POINT |
| Point of Discontinuity | the number that causes the denominator to equal zero (the value of x that causes the denominator to - 0) |
| Steps to find point of discontinuity for the following equation: y = 1/x2 +2x +1 | 1. only use denominator2. set denominator equal to zero3. Solve by factoring or using quadratic equation4. zero product property5. solve for x |
| Is there a point of discontinuity if if x is not a real number? | No |
| What is a hole in a graph? | When the same number in the numerator and denominator cause the equation to equal zero, but there an additional rational function left in the denominator. |
| Where is there a vertical asymptote and no hole? | When the same number in the denominator and numerator equal zero and no additional rational functions |
| When the numerator and denominator of a rational expression are polynomials with no common divisors, the ration expression is _______? | In its simplest form |
| A part of the graph of an inverse varation is called a(n) | Branch |
| If a is a zero of the denominator of a function, the function has a(n) ______ at x = a. | Point of discontinuity |
Created by:
atownley