1. **Functions, Domain, and Range** - A function assigns each input exactly one output. - Domain: all possible input values. - Range: all possible output values. 2. **Function Notation** - Written as $f(x)$, meaning the function $f$ evaluated at $x$. 3. **Eight Basic Functions** - Examples: constant, linear, quadratic, cubic, absolute value, square root, exponential, logarithmic. 4. **Transformations and Reflections** - Shifts: $f(x) + c$ moves graph up/down. - Reflections: $-f(x)$ flips over x-axis. - Horizontal shifts: $f(x - d)$ moves graph right/left. 5. **Inverse Functions** - Reverse the input and output. - To find inverse, swap $x$ and $y$ and solve for $y$. 6. **Simplifying Rational Functions** - Factor numerator and denominator. - Cancel common factors. 7. **Multiplying and Dividing Rational Expressions** - Multiply numerators and denominators. - Divide by multiplying by reciprocal. 8. **Adding and Subtracting Rational Expressions** - Find common denominator. - Combine numerators over common denominator. 9. **Equivalent Rational Expressions** - Expressions that simplify to the same form. 10. **Quadratics and Completing the Square** - Standard form: $ax^2 + bx + c$. - Complete the square: rewrite as $a(x-h)^2 + k$ to find vertex. 11. **Radicals** - Simplify entire and mixed radicals by factoring out squares. - Operations: add, subtract, multiply, divide radicals with same index. 12. **Solving Quadratic Equations and Finding Zeros** - Methods: factoring, completing the square, quadratic formula. 13. **Linear-Quadratic Systems** - Solve by substitution or elimination. 14. **Families of Quadratic Functions** - Parabolas with different $a$, $h$, $k$ values. 15. **Trigonometry Basics** - Ratios: sine, cosine, tangent. - Special triangles: 30-60-90 and 45-45-90. 16. **Trig Identities** - Pythagorean: $\sin^2 x + \cos^2 x = 1$. 17. **Solving Trig Equations** - Use identities and inverse trig functions. 18. **Sin and Cos Law, Ambiguous Case** - Law of Sines and Cosines for any triangle. 19. **Sinusoidal Functions** - Form: $y = A \sin(B(x - C)) + D$. 20. **Rational Exponents** - $a^{m/n} = \sqrt[n]{a^m}$. 21. **Periodic Functions** - Functions that repeat values in intervals. 22. **Graphing Cosine and Sine Functions** - Use amplitude, period, phase shift, vertical shift. 23. **Combinations of Transformations** - Apply shifts, stretches, reflections in order. 24. **Exponential Functions and Equations** - Form: $y = ab^{k(x-d)} + c$. - Growth if $b > 1$, decay if $0 < b < 1$. - Solve by isolating exponential and using logs. 25. **Sequences and Series** - Arithmetic: add constant difference. - Geometric: multiply by constant ratio. - Series: sum of sequence terms. 26. **Pascal's Triangle** - Binomial coefficients useful for expansions. This overview covers all your topics with key formulas and concepts.