Curve Sketching Review

1) Graphing Equations
2) End behavior 
3) Real World Problems
4) Transformations of Graph
5) Write equation of a hyperbola.
6) Write equation of an ellipse.
7) Conic Section type from Diagram
8) Rational Functions Behavior Around Asymptotes x2
9) Solve Rational Inequalities

10) Properties of Logarithms

11) Solve Exponentials

12) Converting to & from Parametric Equations

13) Graph Parametric Equations

14) Composite Functions

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15) Polar Equations

16) Arithmetic and Geometric series in recursive notation.

17) Arithmetic and Geometric series in sigma notation.

18) nth Term of a Geometric series

19) Evaluate Finite sums using sigma notation.

1) Get the power by itself by solving for it.

2) Use the inverse logarithm of the base to get the exponent by itself.

3) Solve the resulting equation.

 $\log_b\left(b\right)=1$  
 $\log\left(mn\right)=\log\left(m\right)+\log\left(n\right)$  
 $\log\left(\frac{m}{n}\right)=\log\left(m\right)-\log\left(n\right)$  
 $\log\left(m^n\right)=n\log\left(m\right)$  
 $\log_b\left(m\right)=\frac{\log_c\left(m\right)}{\log_c\left(b\right)}$  or  $\log_b\left(m\right)\cdot\log_c\left(b\right)=\log_c\left(m\right)$  

 $f\left(x\right)=3x$  &  $g\left(x\right)=2x^2-3$  
 $f\ \circ\ g\left(x\right)=f\left(g\left(x\right)\right)=3\left(2x^2-3\right)=6x^2-9$  
 $g\ \circ f\left(x\right)=g\left(f\left(x\right)\right)=2\left(3x\right)^2-3=18x^2-3$