Higher Order Functions

Question 1

Division Statement

Answer 1

• f(x)/d(x) = q(x) + r(x)/d(x)
• f(x) = q(x) * d(x) + r(x)

Question 2

Division Statement Symbols

Answer 2

• q(x): Dividend
• d(x): Divisor
• r(x): Remainder

Question 3

Properties of r(x)

Answer 3

Has at least one degree less than d(x)

Question 4

Remainder Theorem

Answer 4

f(x)/(ax - b) → remainder = f(b/a)

Question 5

Integral Zero Theorem

Answer 5

• f(b/a) = 0
• a is factor of leading coefficient
• b is factor of constant

Question 6

Behavior of (x - h)^1

Answer 6

Crosses the x-axis

Question 7

Behavior of (x - h)^n, n > 1 and is even

Answer 7

Tangent to the x-axis

Question 8

Behavior of (x - h)^n, n > 1 and is odd

Answer 8

Tangent to and crosses the x-axis

Question 9

Sum and Root (Cubic Function)

Answer 9

• Sum = -b/a = l + m + n
• Product = -d/a = lmn
• c/a = lm + mn + ln

Question 10

Unique Roots Property

Answer 10

• r1 = a + bz, r2 = a - bz
• Where z is an imaginary number or rational exponent

Question 11

Odd or Even Order Function

Answer 11

• Highest degree of function is either even or odd
• Even: Even order function
• Odd: Odd order function