Functions

Question 1

Compound Interest Formula

Answer 1

f(t) = P (1 + r/n)^nt

Question 2

log_b1 =

Answer 2

0

Question 3

log_bb =

Answer 3

1

Question 4

log_bb^p =

Answer 4

p

Question 5

log_bMN =

Answer 5

log_bM + log_bN

Question 6

log_b(M/N) =

Answer 6

log_bM - log_bN

Question 7

log_bM^p =

Answer 7

p log_bM

Question 8

Exponential Growth or Decay Formula

Answer 8

f(t) = a(1 + r)^t

• a is the current or initial count
• r is the growth or decay rate
• t is time.

Question 9

Identify the Function

Answer 9

Absolute Value Function

Question 10

Identify the Function

Answer 10

Cubic Function

Question 11

Identify the Function

Answer 11

Identity Function

Question 12

Identify the Function

Answer 12

Linear Function

Question 13

Identify the Function

Answer 13

Square Root Function

Question 14

Identify the Function

Answer 14

Quadratic Function

Question 15

Identify the Function

Answer 15

Logarithmic Function

Question 16

Identify the Function

Answer 16

Exponential Function

Question 17

Identify the Function

Answer 17

Step Function

Question 18

Rule for translating a function horizontally

Answer 18

f(x ± k)

• • k shifts right
• • k shifts left

Question 19

Rule for translating a function vertically

Answer 19

f(x) ± k

• • k shifts up
• • k shifts down

Question 20

Rule for stretching or compressing a function vertically

Answer 20

(k × f(x))

• k > 1, stretch
• 0 k < 1, compress
• - k, reflected about x-axis

Question 21

Rule for stretching or compressing a function horizontally

Answer 21

( f(k × x))

• k > 1, compress
• 0 k < 1, stretch
• • k, reflected about y-axis

Question 22

Theorem that states every non-constant, single variable polynomial has exactly as many roots as the polynomial’s highest exponent.

Answer 22

Fundamental Theorem of Algebra

Question 23

Theorem which states that if a polynomial finction f(x) is divided by a binomial x-a, where a is a real number, the remainder of the division will be the value of f(a). If f(a) = 0, then a is a root of the polynomial.

Answer 23

Remainder Theorem

Question 24

Theorem which states that if f(a) = 0 then (x - a) is a factor of the function.

Answer 24

Factor Theorem

Question 25

Theorem which states that any rational root of a polynomial function

f(x) = a_nxⁿ + a_n-1x^n-1 + … + a₁x + a₀

with integer coefficients will, when reduced to its lowest terms, be a positive or negative fraction such that the numerator is a factor of a₀ and the denominator is a factor of a_n.

Answer 25

Rational Root Theorem

Question 26

Define these properties of functions:

1. End Behavior
2. y-intercept
3. Roots
4. Extrema

Answer 26

1. The behavior of the function at extreme values (f(x) as x → ± ∞)
2. The value of the function at f(0)
3. The value of x where the function equals zero (f(x) = 0
4. Minimum or maximum values of the function or where the function changes direction (f(x) ≥ k) or (f(x) ≤ k)

Question 27

Define:

Function

Answer 27

A relation in which each value of x has exactly one value for y on the coordinate plane.

Question 28

Define:

One-to-one Function

Answer 28

A relation in which each value of x has exactly one value for y on the coordinate plane and each value of y has exactly one value for x.

The vertical line test will determine if a graph is a function.

The horizontal line test will determine if it is one-to-one.

Question 29

Define:

Many-to-one Function

Answer 29

A function whereby the relation is a function, but the inverse of the function is not a function. Each element in the domain is mapped to one and only one element in the range. However, one or more elements in the range may be mapped to the same element in the domain.

Question 30

Define:

Monotone Function

Answer 30

A function whose graph either constantly increases or constanyly decreases.

Question 31

Define:

Even Function

Answer 31

A function whose graph is symmetric with respect to the y-axis and satisfies the equation f(x) = -f(-x).

Question 32

Define:

Odd Function

Answer 32

A function whose graph is symmetric with respect to the origin and satisfies the equation f(x) = -f(-x).

Question 33

Define:

Constant Function

Answer 33

A function given by the equation f(x) = b where b is a real number. There is no independent variable present in the equation, so the function has a constant value for all x.

Question 34

Define:

Identity Function

Answer 34

A function defined by the equation f(x) = x, where every value of the function is equal to its corresponding value of x. The only zero is the point (0,0). The graph is a line with slope of 1.

Question 35

Define:

Linear Function

Answer 35

A function whose value changes in direct proportion to x. The rate of change, represented by the slope of its graph, is constant throughout.

Question 36

Define:

Algebraic Function