FUNCTIONS
COORDINATE GEOMETRY
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.
71 . 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 the fraction 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.
72 . Finding the Distance Between Two Points
