Math 1050 Final Review Quadratic Functions o How

Math 1050 Final Review

Quadratic Functions o How do you find the vertex? o How do you know if it opens up or down? o How do you determine max or min? o (Inequalities) Graph (x+2)2 -1 <0

Functions o How do you find domain and range? o How do you know if function is even or odd? o How do you find the inverse of a function? o How do you show 2 functions are inverses? o What is a one-to-one function? o fog and go f o Difference quotient

Graphing techniques o HI VO transformations: (horizontal inside) vertical outside o Study families of graphs o Can you find f(-3) on this graph? o What do piecewise functions look like?

Polynomials o How do you form a polynomial when given real zeros and degree? o How do you find real zeros? n Rational zeros them n Synthetic division n Factoring and quadratic formula o What are complex zeros?

Graphs of Polynomials o How do you determine “End Behavior”? o How does multiplicity affect the graph of a polynomial? o How do you determine intercepts?

Rational Functions o How do you find the domain? o How do you find x and y intercepts? o How do you determine asymptotes? n Vertical n Horizontal n Oblique o What do I need to know to graph them? o How do I solve rational function inequalities?

Logarithmic Functions o What does the graph look like? n What are graph main properties? o What are the properties of logs? o What is the Change of Base formula n When is it used? Ex: find log 518? o What is base of ln? n When is it used? Ex: 5 x-2 =33 x+2 o What is domain of a log? o What is logistic model formula?

Exponential Functions o What does graph look like? n What are graphs main properties? o What are some important properties of exponential functions? o What is the Exponential Law (Law of Uninhibited Growth? ) o What are all the Interest formulas?

Parabola o What are the general formulas for parabolas (opening left/right and up/down) o How far away are directrix and focus from the vertex? o How do you find 2 points on the Latus Rectum? o Ex: Find equation if vertex =(-2, 3) focus = (0, 3)

Ellipse o What are the general formulas? o How far are vertices and focus from the center?

Hyperbola o What are general formulas? o How far away are vertices and focus from the center? o What are the equations of the asymptotes?

Circles o What is the general equation for a circle? o How do you complete the square to get it in this form? o How do you know the center of a circle?

Matrices o How do you find the determinant of a 2 x 2 and a 3 x 3 matrix? o How do you multiply matrices? o How do you use an inverse matrix to solve a system of equations? o How do you do row operations? o How do you find inverse matrix? o How do you use Cramer’s Rule?

Sequences o How is arithmetic different than geometric? o How do you find the nth term of an arithmetic or geometric sequence? o How do you find the summation of n terms for an arithmetic or geometric sequence? o How do you know if geometric sequence converges or diverges? n Converges to what? (what’s the formula? )

Partial Fraction Decomposition o What are the 4 cases?