fx A Function Family Album Kinds of Functions

f(x) A Function Family Album

Kinds of Functions Names Graphs �Linear �Straight Line � Constant � Horizontal Line � Identity � Slanted Line �Quadratic �Parabola �Cubic �Half Parabola �Exponential �Twisted Parabola �And many more!

How can you tell if it is Linear? �Graph is a non-vertical straight line �No exponents higher than one �No operations except addition, subtraction, and multiplication �No variables multiplied together �No variables in a denominator �Must be able to put it in the form f(x) = mx + b (where b is a constant and m is a coefficient) The first number is obviously 4

Is it Linear? �f(x) = 4 x² + 4 �g(x) = ½ x – 9 �r(x) = √x + 3 �k(x) = kx – 7 �x = 6 Why or why not?

Ways to Describe Linear Functions Term Definition �Domain �All Real Numbers �Range �All Real Numbers (unless �Y –Intercept �Slope horizontal line) �Point where line crosses the y. The second axis number is �Change in Y/Change in X obviously 7

Graphing a Linear Function �Example: f(x) = 2 x + 4 x -3 -1 0 1 2 x + 4 f(x) (x, y)

Two Kinds of Linear Equations Identity Function Constant Function �Parent Function: f(x) = x �Parent Function: f(x) = c �Graph: slanted line �Graph: horizontal line �Domain: All Real Numbers �Range: All Real Numbers �Y-Intercept: constant �Slope : coefficient of x Numbers �Range: c �Y-Intercept: c �Slope : zero The third number is obviously 5

Describe the Linear Function �Domain? �Range? All Real Numbers (-∞, +∞) �Y-Intercept? �Slope? 3 3/4 �Equation? g(x) = ¾ x + 3