Honors Alg2 / Trig - Chapter 2 Miss Magee / Fall 2007 (graph paper will be needed for this chapter)

2.1 – Functions and Their Graphs (p.67) A)Definitions: * Relation - any set of ordered pairs * Domain – all of the x-values (input) * Range – all of the y-values (output) * Function – a relation in which each x- value has only ONE y-value (one output for each input)

2.1 (cont) B) A relation is NOT a function if:  1) x-value repeats  2) vertical line test (vertical line can’t intersect the graph at more than one point)  3) more than one arrow from each domain #  Ex: (1) (-3,1), (2,3), and (3,-2) plot these points D= {-3,2,3} R= {-2,1,3}

2.1 (cont) Ex: (2) plot the following ordered pairs (-4,-2), (-2,1), (-2,3), (1,1), and (2,-2) D = {-4, -2, 1, 2} R = {-2, 1, 3} Determine whether this is a function. Check: (1) x-value repeats (2) vertical line test (3) more than one arrow from each domain # Answer: This is NOT a function!

2.1 (cont) C) Functions can be represented by an equation in two variables. Linear function: y = mx+b or f(x) = mx+b An ordered pair is a solution when the equation is true if x and y are substituted into the equation. EEx: y = 2x - 7 or f(x) = 2x – 7 Check to determine if (2,-3) is a solution. Answer: Yes. y = 2x – 7 (-3) = 2(2)-7 -3 = 4 – 7 -3 = -3

2.1 (cont) Graphing Steps:  (1) Set up an x|y table  (2) Graph the ordered pair.  (3) Connect the points w/ a line or curve. Ex: Graph the given function: (follow the above steps) Ex. 1) y = -x - 1

2.1 (cont) D) Evaluating Functions  Decide whether the function is linear and evaluate for the given value. Ex: (1)when x = 2 No, this is a quadratic function. (2) g(x) = 3|x| - 4 when x = -3 No, 3(3) – 4 = 5.

2.2 Slope and Rate of Change (p.75) A) Slope – a characteristic of a line; ratio of vertical to horizontal change. Ex: (Find the slope)  (1) (6,2) and (3,-4)  (2) (6,2) and (6,8)  (3) (6,2) and (7,2)

2.2 - See overhead  B) Line Classification

2.2 (cont) C) Determining Steepness  The line w/ greater slope is steeper.  The line w/ the slope of greater absolute value is steeper. Ex:  Line 1: thru (-1,-3) and (-3,-2)  Line 2: thru (3,-4) and (0,-3) Answer: Line 1 is steeper.

2.2 (cont) Parallel lines - two lines that do NOT intersect; same slope. Perpendicular lines – two lines that intersect to form a right angle; slopes are negative reciprocals of one another.

2.3 Quick Graphs of Linear Equations A) Slope Intercept Form  Y=mx+b m=SLOPE b= y-intercept Steps: (1) Solve equation for y. (2) Plot the y-intercept (3) Use the slope to plot a second point. (4) Draw a line thru the two points (use arrows).

2.3 (cont B) Standard Form  Ax+By=C m = -A/B Steps: (1) Arrange equation into Ax+By=C form (2) Find y-intercept and plot point. (x+0) (3) M = -A / B (4) Draw a line thru the points.