Definitions
The simple definition of a function
For every input (x) there is exactly ONE output (y)
State is the Pythagorean Theorem
a2+b2=c2
sine, cosine, tangent
If (x-1) is a factor of 2x²+kx-5, what is “k”?
k=3
What does this symbol represent?
ℝ
All real numbers
State the quadratic formula
x=−b±√b2 - 4(ac)/2a
What relationship does cosecant, secant, and cotangent have with the basic 3 ratios?
They are the reciprocal functions
Rewrite log5(125)=3
53=125
What is an inverse function?/What does it do?
"undoes" or reverses another function
f(x) -> f-1(x)
What is the factor theorem in polynomials?
The polynomial x − a is a factor of P(x) if and only if P(a) = 0
State the first main pythagorean identity
sin2θ+cos2θ=1
Find the inverse function:
f(x)=3x2-1
f-1(x)=√(x+1)/3
The discriminant of a quadratic equation, b2-4ac, tells us what?
The number and type of solutions to the equation
How are exponential and logarithmic equations related?
They are inverses of each other
What is a radian?
The angle formed when an arc length is the same as the radius of the circle
Solve:
4+i/8+9i
41-28i/145
What is i?
An imaginary number representing √-1
How do you solve radical equations?
Isolate the radical, eliminate it, solve the new equation, and check
A right triangle has an angle of 30° and the adjacent side is 10 units. Find the opposite side.
O≈ 5.77 units.
Solve:
x-2=√2x-4
x=2,4