![]() ![]() The equation y = mx + b becomes y = 0x + 3, or just y = 3. The second piece of the graph has a y-intercept of 3 and a slope of 0. The equation y = mx + b becomes y = x + 3.Ģ. The first piece of the graph has an y-intercept of 3 and a slope of 1. The second piece of the graph occurs between x = 0 and x = 3.ġ. The first piece of the graph occurs between x = -3 and x = 0.Ģ. ![]() We also need to state the x-coordinates that the graph's pieces lie between along with each equation.įirst, let's state the 2 pieces' x-coordinates:ġ. Since both pieces are straight we will use y = mx + b to describe them. There are 2 pieces to our graph so we will need to write two equations to describe it. If the graph has a V-shape, we will use y = | x | If the graph is a curve, we will use y = ax 2 + bx + c If the graph is a straight line, we will use y = mx + b We use this information to describe the graph along with each pieces' equation.īetween the x-coordinates 0 and 5, we write 0 ≤ x ≤ 5īetween the x-coordinates of -2 and 3, we write -2 ≤ x ≤ 3īetween the x-coordinates of 4 and 7, we write 4 ≤ x ≤ 7īetween the x-coordinates of 5 and 9, we write 5 ≤ x ≤9 The pieces of the graphs occur between certain x-coordinates. When graphing piecewise functions it is allowable to write an equation of the graph using multiple equations per graph. This is why it's important to memorize the three equations and graph shapes shown at the top of the page. We can use our equations to define certain pieces of the graphs, but no one function can be used to define the whole graph itself. This is where the concept of piecewise functions come from. So how do we find an equation of these graphs? Their "pieces" can be described using equations, but not the entire graph. These graphs are called piecewise functions. Sometimes graphs don't fit into the three categories above due to their shape. The graphs of each function are shown below: When graphing functions, there are several functions you should already be familiar with: ![]()
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