FUNCTIONS
To solve an inequality, do whatever is necessary to both sides to isolate the
variable. Just remember that when you multiply or divide both sides by a
negative number, you must reverse the sign. To solve −5x + 7 < −3,
subtract 7 from both sides to get −5x < −10. Now divide both sides by −5,
remembering to reverse the sign: x > 2.
68 . Radical Equations
A radical equation is one that contains at least one radical expression. Solve
radical equations by using standard rules of algebra. If then
and so x = 9.
69 . Function Notation and Evaluation
Standard function notation is written f(x) and read “f of x.” To evaluate the
function f(x) = 2x + 3 for f(4), replace x with 4 and simplify: f(4) = 2(4) + 3 = 11.
70 . 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.
