Final Flashcards
(35 cards)
A function is increasing on an interval if …
A function is decreasing on an interval if…
A function is concave up if…
A function is concave down if…
Formula and example of average rate of change
A function is linear if…
A function is quadratic if…
End behavior of a polynomial function with an even degree and a negative leading coefficient
A relative/local minimum occurs…
A relative/local maximum occurs…
Multiplicities of Zeros
What is an Even Function?
Symmetrical y-axis
Even highest degree
F(-x) = F(x)
F(x) = X^2
F(-x) = (-x)^2 = x^2
What is an Odd Function?
Rational Functions
1. How do you determine the End Behaviors?
2. How do you find the Horizontal Asymptotes?
3. How do you find the Vertical Asymptotes?
4. How do you determine if there is a slant asymptote?
5. How do you determine if there is a hole?
6. How do you determine the domain?
How do you use Pascal’s Triangle to expand (a+b)^4
A function is Cubic if …
A function is Quartic if …
Transformations of functions
Vertical Shift - F(x) + C [moves up when c>0, moves down when c<0]
Horizontal shift - F(x+c) [moves right when c<0 moves left when c>0]
Vertical Dilatation - C x f(x) [Dilatation factor: |c|
Stretches y-direction when |c|>1
Shrinks when 0<|c|<1
Horizontal Dilation - F(c(x)) [Dilation Factor: |1/c| Shrinks x-direction when |c|>1
Stretches when 0<|c|<1
Reflection over x-axis -
-F(x) [(x,y) - (x,-y)
Reflection over y-axis - F(-x) [(x,y) - (-x,y)
Point of inflection
A point of inflection is where concavity changes (steepest slope)
Absolute minimum/maximum
How can you use multiplicities of zeros to graph a polynomial function?
End behavior of a polynomial with an odd degree and a positive leading coefficient
End behavior of a polynomial with an odd degree and a negative leading coefficient.
End behavior of a polynomial with an even degree and a positive leading coefficient
