A family of functions is a group of functions with similar characteristics. For example, functions in the form of f(x) = mx + b constitutes the family of linear functions.f(x) = xIs called theparent linearfunction.y=x
EXAMPLE 4 Compare graphs with the graph f (x) = x Graph the function. Compare the graph with the graph of f (x) = x. g(x) = x + 3 SOLUTION Because the graphs of g and f have the same slope, m = 1, the lines are parallel. Also, the y- intercept of the graph of g is 3 more than the y- intercept of the graph of f.
EXAMPLE 4 Compare graphs with the graph f (x) = x h(x) = 2x SOLUTION Because the slope of the graph of h is greater than the slope of the graph of f, the graph of h rises faster from left to right. The y-intercept for both graphs is 0, so both lines pass through the origin.
GUIDED PRACTICE an equation from a graph Write Graph h(x) = – 3x. Compare the graph with the graph of f (x) = x. SOLUTION Since the slope of the graph of h is negative the graph of h falls from left to right. The y- intercept for both graphs is 0, so both lines pass through the origin.
What is the linear function that matchesthis graph? Compare it to f(x) = x
Assignment: Cont’ P. 266 (#23-26, 29- 31, 39-41)
Big Ideas for the Quiz Find the slope – given two points Find the slope – given a graph Tell if an equation represents “direct variation” – if so, give the constant of variation. Given an equation, find the slope and y- intercept. Decide if two functions / equations are parallel (without graphing)
Re-write an equation in slope-intercept from Word problem – graph and compare Given an equation, write another equation that will parallel to that one.