ALGEBRA II CHAPTER 9 NOTES RATIONAL EQUATIONS AND FUNCTIONS Name
Algebra II 9. Graphing Simple Rational Functions Day One Today I am graphing simple rational functions. I am successful today when I can graph simple rational functions. It is important for me to know/do this because graphs of simple rational functions can help solve real-life problems. 1. Graph the function 1 y -intercept: domain: range: Asymptote: a line that is approached by the graph. The distance between the graph and the line approaches zero. The graph of 1 y is called a HYPERBOLA. It is a rational function in the form of h and y k. Hyperbolas have asymptotes of a y k h To find the y-intercept, plug 0 in for and solve for y. To find the -intercept, plug 0 in for y and solve for. Plot a few more points on each side of the vertical asymptote to get a graph. The graph will have two branches... Graph the function y 3 -intercept: domain: range:
3. Graph the function y 1 3 1 -intercept: domain: range: 4. Graph the function y 1 3 4 -intercept: domain: range: Homework: 9. Day One Worksheet
Algebra II 9. Graphing Simple Rational Functions Day Two Today I am graphing simple rational functions. I am successful today when I can graph simple rational functions. It is important for me to know/do this because graphs of simple rational functions can help solve real-life problems. Rational functions can also take the form a b y c d. These graphs are also called hyperbolas. The vertical asymptote occurs at the -value that makes the denominator zero. So, solve the denominator for zero. a The horizontal asymptote is the line y. c To find the y-intercept, plug 0 in for and solve for y. To find the -intercept, solve for the numerator for zero. Plot a few more points on each side of the vertical asymptote to get a graph. The graph will have two branches. 1. Graph the function y 3 3 -intercept: domain: range:. Graph the function y 4 -intercept: domain: range:
3. Graph the function y 5 -intercept: domain: range: Homework: 9. Day Two Worksheet
Algebra II 9.3 Graphing General Rational Functions Today I am graphing general rational functions. I am successful today when I can graph general rational functions. It is important for me to know/do this because graphs of general rational functions can help solve real-life problems. Graphs of Rational Functions f p q am b n m n...... The -intercepts (where graph crosses -ais) are the real zeros of p(). The graph of f has a vertical asymptote at each real zero of q(). The graph of f has at most one horizontal asymptote if m < n ( ), the line y 0 (-ais) is a horizontal asymptote. am if m = n ( ), the line y is a horizontal asymptote. b (Reduce the coefficients in front of the variables) if m > n ( ), the graph has no horizontal asymptote. am mn The graph s end behavior is the same as the graph of y. b n n y 1. 4 -intercept:. y 4 1 -intercept:
3. 6 y -intercept: 4. y 8 4 9 -intercept: Homework: 9.3 Worksheet
Algebra II Factoring Review for 9.4 Notes 1. 6 8. 9 8 3. 8 4. 7 8 5. 9 6. 5 16 7. 3 8 8. 3 7 64 9. 6 11 4 Homework: Factoring Review worksheet
Algebra II 9.4 Multiplying and Dividing Rational Epressions Today I am multiplying and dividing rational epressions. I am successful today when I can multiply and divide rational epressions. It is important for me to know/do this because rational epressions can model real-life quantities. Simplifying rational epressions requires two steps: Factor the numerator and denominator (if possible) Divide/cancel out any factors they have in common 1. 5 9 6 5 5 7 18. 6 y 10 y y 18y 3 3 4 3. 9 y 1 y 3 3 y 7y 3 4 5 4. 56 1 5. 3 14 36 1618 6. 3 7 8 3 1310 7. 9 4 4 4 6 3 8. 16 41 3 64 1
9. 3 3 4 8 6 10. 4 1 5 3 5 4 3 3 3 11. 4 1 16 1 Homework: 9.4 Day One Worksheet
Algebra II 9.5 Day 1 Addition, Subtraction, and Comple Numbers Today I am adding and subtracting rational epressions and simplifying comple fractions. I am successful today when I can add and subtract rational epressions. It is important for me to know/do this because rational epressions can model real-life quantities. ***IN ORDER TO ADD/SUBTRACT FRACTIONS, YOU MUST HAVE A COMMON DENOMINATOR*** 1. 1 5. 18 18 4 5 3. 3 3 5 1 4. 1 8 4 3 3 5. 3 1 6 4 4 6. 1 1 1 7. 8 4 8. 6 4 31 5 9. 4 3 6 3 3 3
10. 1 4 4 4 11. 1 1 6 9 9 Homework: 9.5 Day One Worksheet
Algebra II 9.5 Day Addition, Subtraction, and Comple Numbers Today I am adding and subtracting rational epressions and simplifying comple fractions. I am successful today when I can add and subtract rational epressions. It is important for me to know/do this because rational epressions can model real-life quantities. ***IN ORDER TO ADD/SUBTRACT FRACTIONS, YOU MUST HAVE A COMMON DENOMINATOR*** 1. 1 3 4. 1 1 1 3 3. 3 1 1 4. 1 4 1 1 5. 3 4 1 3 4 1 Homework: 9.5 Day Two Worksheet
Algebra II 9.6 Solving Rational Equations Today I am solving rational equations. I am successful today when I can solve rational equations. It is important for me to know/do this because rational equations can help solve real-life problems. ***Be careful when solving you may get etraneous solutions. Plug your answer back in to the original equation to make sure it works and WATCH THAT YOU DO NOT GET DIVISION BY ZERO.*** 1. 1 6 4. 1 4 4 3. 5 10 7 4. 3 1 1 5. 5 5 4 1 1
6. 18 3 3 9 7. 3 5 15 0 1 6 7 6 Homework: 9.6 Day One Worksheet