chapters 2 - 7

# Chapter 2 ### *2-1 Relations and Functions*: \* a function rule is an equation that represents an output value in terms of an input value. You can write a function rule in the function notion ex \[Outputs: y, f(x), C, &, etc. \[Inputs: x, or any other variables --- Flashcard 9 ^^EX. Tickets to a concert are available online for $35 each plus a heading fee of $2.50. The total cost is a function of the number of tickets bought. What function rule models the cost of the concert tickets? Evaluate the function for 4 tickets.^^ Answer: Independent = # of tickets bought (x) Dependent = Total cost of everything (y) --- --- ### *2-2 Direct Variation*: You can write a formula for a direct variation function as y=kx, or y/x = k, where k = 0. x represents input values, and y represents output values. The Formula y/x says that, except for (0,00, the radio of all output-input pairs equals the constant k, the constant of variation. \ In direct variation, y/x is the same for __all__ pairs of data where x = 0. So \[y1/x1 = y2/x2\] is true for the ordered pairs (x1, y1) and (x2, y2), where neither x1 nor x2 is zero --- ### *2-3 Linear function and Slope - Intercept Form:* \[Slope - is also denoted with the letter __*m*__. The slope is the “rate of change”.\] a function whose graph is a line a linear function. You can represent a linear function with a linear equation, such as y=6x -4. A solution of a linear equation is any ordered pair (x,y) that makes an equation true. There are different special forms of the linear equation: slope-intercept form and point-slope forms. --- ### *2-4 0 y = f(x) + k * translation down by k units, k>0 y = f(x) - k * \ * **Vertical stretches and compressions** * vertical stretch, a >1 y = af(x) * vertical compressions, 0