FUNCTIONS
Function Notation and Evaluation
Standard function notation is written f(x) and read “f of 4.” To evaluate the function f(x) = 2x + 3 for f(4), replace x with 4 and
simplify: f(4) = 2(4) + 3 = 11.
Direct and Inverse Variation
In direct variation, y = kx, where k is a nonzero constant. In direct variation, the variable y changes directly as x does. If a unit of
Currency A is worth 2 units of Currency B, then A = 2B. If the number of units of B were to double, the number of units of A would
double, and so on for halving, tripling, etc. In inverse variation, xy = k, where x and y are variables and k is a constant. A famous
inverse relationship is rate × time = distance, where distance is constant. Imagine having to cover a distance of 24 miles. If you
were to travel at 12 miles per hour, you’d need 2 hours. But if you were to halve your rate, you would have to double your time.
This is just another way of saying that rate and time vary inversely.
Domain and Range of a Function
The domain of a function is the set of values for which the function is defined. For example, the domain of is all
values of x except 1 and −1, because for those values the denominator has a value of 0 and is therefore undefined. The range of a
function is the set of outputs or results of the function. For example, the range of f(x) = x^2 is all numbers greater than or equal to zero,
because x^2 cannot be negative.