1. Cochino’s Math
By Jocelyn Hernandez, Leslie
Zamudio, Horacio Sevilla & Yesenia
Gonzalez

2. Functions and Their Graphs
• Properties of Lines
• Slope m=y2-y1/x2-x1,
• Point slope y-y1=m(x-x1), Slope Intercept
y=mx+b
• Vertical X=Y Horizontal Y=X

3. Basic Functions, Functions and Graphs
• Function: A function has a value in the domain with exactly
one value in the range
• Domain: The input or (x)
• Range: The output or (y)
• Vertical line test: if it passes it’s a function
• Solving for a function: Algebraic, Numeric or Graphically
• Continuity of a graph: Contiguous
• Increasing and decreasing graphs.
• Asymptotes: a line that a graph approaches but never
reaches

4. Transformations (Shifts, Stretches, and
Reflections)
• Horizontal Translations:
• Y=f(X-C) Translation to the right by C units
• Y=f(X+C) Translation to the left by C units
• Vertical Translations:
• Y=F(X)+C Translation up by C units
• Y=F(X)-C Translation down by C units
• Reflections across the X-axis: y=-f(x)
• Reflections across the Y-axis= f(-x)

5. Transformations (Shifts, Stretches, and
Reflections)
• Stretches and Shrinks:
• Horizontal: Y=F(X/C) {A stretch by a factor of C
if C>1}
• {a shrink by a factor of C if C<1}
• Vertical: Y=C*F(X) {A stretch by a factor of C if
C>1}
• {A shrink by a factor of C if C<1}

6. Combination of Functions
• Sum: (F+G)=F(X)+G(X)
• Difference: (F-G)(X)=F(X)-G(X)
• Product: (FG)(X)=F(X)*G(X)
• Quotient: (F/G)(X)=F(X)/G(X), Provided G(X)
cannot equal 0

7. Polynomials and Rational Functions
• Ways to solve a Quadratic Equation: Factoring,
Using the Quadratic Formula, Completing the
Square ax2 + bx = c
• Polynomial Function
• One-To-One Functions
• Horizontal Line Test
-If some horizontal line intersects the graph of
the function more than once,then the function is not
one-to-one.
-If no horizontal line intersects the graph of the
function more than once,then the function is one-to-one.

8. Polynomials and Rational Functions
• Synthetic Division:
• Real zeros and complex numbers
-complex numbers are numbers such as :
4+3i , 5i+i etc...
• real zeros are the intercepts of a quadratic
equation

9. Polynomials and Rational Functions
• Rational Functions :To graph a rational
function, you find the asymptotes and the
intercepts, plot a few points, and then sketch
in the graph example equation:

10. Polynomials and Rational Functions
• Fundamental Theorem of Algebra
• Any polynomial of degree n ... has n roots, but
you may need to use complex numbers example
of a polynomial
• this one has 3 terms
• The Degree of a Polynomial with one variable is
the largest exponent of that variable.

11. Synthetic Division

12. Analytical Geometry
• Parabolas
•
F(x)=x^2

13. Exponential and Logarithmic Functions
• Exponential Function : f(x)=a.
bx
• Logarithmic Function:
y= Logbx
• Properties of Logs:
• Product: logbMN=logbM+logbN
• Quotient: LogbMN=logbM-LogbN
• Power: LogbNy=ylogbN

14. Exponential and Logarithmic Functions
• Basic Common Logarithms Functions:
• -Log101=0 because 100=1
• -Log1010=1 because 101=10
• -Log1010y=y because 10y=10y
• -Loglogx=x because Logx=logx
• Log always finds the exponent!!

15. Ellipses with center(0,0)

16. Ellipses with center (h,k)

17. Hyperbolas

18. Hyperbolas center (0,0)

19. Hyperbolas center (h,k)