How do you break up I x + 1 I > y?
- x + 1 > y
- x + 1 < -y
What is the determinant of a 2 by 2 matrix?
ad-bc
How do you do matrix multiplication?
Left row by right column
Standard Deviation
What is the arithmetic sum?
What is the pythagorean identity?
sin(x) + cos(x) = 1
What is cosecant (csc)?
1/sin(x)
What is secant (sec)?
1/cos(x)
What is cotangent (cot)?
1/tan(x)
What is sin(x)/cos(x)?
tan(x)
What is cos(x)/sin(x)?
cot(x)
What are the 3 horizontal asymptote rules
Let N = the largest indicy in the numerator
Let D = the largest indicy in the denominator
- If N > D there is no horizontal asymptote
- If N = D the horizontal asymptote is y = the ratio of leading coefficients
- If N < D the horizontal asymptote is y = 0
When does a vertical asymptote occur?
When ONLY the denominator equals 0
When do holes occur (asymptotes)
When both the denominator and the numerator equal 0
When do x intercepts occur in asymptotes?
When only the numerator equals 0
What is an even function?
f(-x) = f(x) — symmetric across the y-axis
What is an odd function
f(-x) = -f(x) — reflected across the origin
Give 4 examples of odd functions
- sin(x)
- csc(x)
- tan(x)
- cot(x)
Give 2 examples of even functions
- cos(x)
- sec(x)
What is the standard form of a quadratic equation?
y = ax^2 + bx + c
How do you find the vertex from the standard quadratic form?
- To find the x-coordinate of the vertex: x=-b/2a
- To find the y-coordinate of the vertex: plug the x-coordinate back in
What is the factored/intercept form of a quadratic equation?
y = a(x - m)(x - n)
How do you find the vertex from the factored form?
- The vertex is halfway between the 2 x-intercepts
- average the x intercepts to find the x
- plug the x back into to find the y
What is the vertex form of a quadratic equation?
y = a(x - h)^2 + k
