Msec equation
(f(b) - f(a)) / (b - a)
What is the leading coefficiant
AnX^n + An-1X^n-1 + … + A1X^1 + A0
AnX^n
How many possible turning points does the following have
2x^3 - 3x^2 + 4
2
What is the degree of the following
2x^3 - 3x^2 + 4
3rd
How can you tell if a function is even
if f(-x) = f(x)
How can you tell if a function is odd
if f(-x) = -f(x)
Can you have a function that is neither even nor odd
Yes
is f(x) = x^2 - 5 an even or odd function
f(-x) = (-x)^2 - 5 = x - 5, even
is f(x) = 5x^3 - x an even or odd function
f(-x) = 5(-x)^3 + x = -5x^3 + x = -1(5x^3 - x), odd
If a factor’s multiplicity os odd, does it go through the x-axis on a graph or does it bounce
It goes through
If a factor’s multiplicity os even, does it go through the x-axis on a graph or does it bounce
It bounces
What is a dividend
The numerator
What is a devisor
The demoninator
What are the zeros of the following function:
f(x) = (x + 6)(x - 1)(2x + 1)
x = -6, 1, -1/2
What is another word for ‘complex’
Imaginary
What translations happen in the following function:
f(x) = -3 f(2(x + 1/2)) + 5
Left 1/2, horizontal compression by 1/2, reflect over the x-axis, vertical stretch by 3, and up 5
What do you do to a fraction function to find domain
Set the denominator = to 0 and solve for x
what is the domain of the following function:
f(x) = (3x^2) / (x^2 + 1)
x^2 + 1, x^2 = -1, x = +- i, D = All real. numbers
What is the VA of the following function:
f(x) = (x + 3) / (x - 1)
x - 1, x = 1, VA: x = 1
What is the HA of the following function:
f(x) = (x + 3) / (x - 1)
Neither numerator nor denominator have an int in front of them in factored form, so 1 / 1 = 1, HA: y = 1
Does the following function have a hole:
f(x) = (x + 3)(x - 3) / (x + 7)(x - 3)
yes, the (x - 3) on the numerator and denominator cancel out, leaving a hole at x = 3
What happens to the graph if the multiplicity of the VA factor is odd
the graph approaches x = ∞ on one side and approaches x = -∞ on the other
What happens to the graph if the multiplicity of the VA factor is even
The graph approaches either + or - ∞ on both sides
What is the behavior of the asymptote if n < m
HA: y = 0
