The+Rest+of+Chapter+1+Notes

Linear Function - f(x)= mx + b Constant Function - f(x)= b Identity Function - f(x)= x Square Function - f(x)= x^2 Cube Function - f(x)= x^3 Square Root Function - f(x) = root of x or f(x)^1/2 Cube Root Function - f(x)= x^1/3 Absolute Value Function - f(x)= absolute value of x Reciprocal Function - f(x)= 1/x Vertical Shifts f(x) + c c units upwards f(x) - c c units downward Horizontal Shifts f(x + c) c units to the left f(x - c) c units to the right Sum (f + g)(x) = f(x) + g(x) Difference (f - g)(x) = f(x) - g(x) Product (f x g)(x) = f(x) x g(x) Quotient (f/g)(x) = f(x) / g(x) g(x) can't equal o One-to-one Function A function f(x) is one-to-one if no two elements in the domain correspond to the same element in the range; that is, if x1 cannot equal x2, then f(x1) cannot equal f(x2) Horizontal line test If every horiz. line intersect the graph of a function in at most one point, then the graph is a one-to-one function Inverse Functions If f and g denote two one-to-one functions such tha**t** f(g(x)) = x for every x in the domain of g and g(f(x)) = x for every x in the domain of f then g is the inverse function of f
 * 1.2 Graphs of Functions**
 * 1.3 Graphing Techniques: Transformations**
 * 1.4 Combining Functions**
 * 1.5 One- To-One Functions and Inverse Functions**