Math Flashcards
What does “ I x I “ represent?
The distance x is from 0
What is “ I x - h I “
The distance x is from h
What is the determinant of the 2*2 matrix (a/c b/d)?
ad-bc
What does “ i “ represent?
Root -1
What is “i squared”
-1
What is the English for asymptote?
Tends towards
What is the English for exponent?
Index (Indicy)
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
What must an absolute value be?
≥ 0
What solution will absolute value that is = -5
No solution since an absolute value is ≥ 0, so it can never equal to a negative
What solution is there to an absolute value that is ≤ -5
No solution since an absolute value is always ≥ 0 so it will never be < or ≤to a negative
What solution will there be to an absolute value that is ≥ -5
Infinite solutions since an absolute value is always 0 so it will always be > than a negative
When is there no horizontal asymptote?
When the largest indicy in the numerator is greater than the largest indicy in the denominator
When is the horizontal asymptote y = 0?
When the largest indicy in the denominator is greater than the largest indicy in the numerator
What is the horizontal asymptote when the largest indicy in the denominator is equal to the largest indicy in the numerator?
The ratio of leading coefficients
When do x intercepts occur in asymptotes?
When ONLY the numerator equals 0
When do vertical asymptotes occur?
When ONLY the denominator = 0
When do holes occur in asymptotes?
When both the numerator and the denominator = 0
How do you find the x value of a hole in an asymptote?
It is the answer
How do you find the y value in holes in asymptotes?
Simplify the equation and plug in the x value
When do slant asymptotes occur?
When the largest exponent in the numerator is 1 greater than the largest exponent in the denominator
how do you find the slant asymptote?
Divide and ignore the remainder
What is the area of a trapezoid?
1/2 (a + b)H
What is the area of a parallelogram?
Base X Perpendicular Height
What are the 2 ways of finding the area of a rhombus?
- Base X Perpendicular Height
- 1/2 diagonal 1 * diagonal 2
What is the volume of a pyramid?
1/3 area of base X height
What is an even function?
f(-x) = f(x)
- When it is symmetric across the y axis
What is an odd function?
f(-x) = -f(x)
- reflected across the origin
What type of function is sin(x)?
Odd
What type of function is csc(x)?
Odd
What type of function is tan(x)?
Odd
What type of function is cot(x)?
Odd
What type of function is cos(x)?
Even
What type of function is sec(x) ?
Even
What is csc(x)?
1/sin(x) - reciprocal of sin(x)
What is sec(x)?
1/cos(x) - reciprocal of cos(x)
What is cot(x)?
1/tan(x) - reciprocal of tan(x)
How do you get to the next term in geometric sequences?
You multiply by the common ratio (r)
How do you find the common ratio in geometric sequences?
By dividing one term by the previous term
