advertisement

2-6 Special Functions Objectives Students will be able to: 1) identify and graph step, constant, and identity functions 2) Identify and graph absolute value and piecewise functions Absolute Value Functions • Let’s continue graphing absolute value equations…. Domain: {all real #’s} Range: {𝑦 𝑦 ≥ 1} Domain: {all real #’s} Range: {𝑦 𝑦 ≥ −2} Domain: {all real #’s} Range: {𝑦 𝑦 ≥ 0} Domain: {all real #’s} Range: {𝑦 𝑦 ≥ 0} Let’s make some conclusions based on our observations… • What happens when a constant is added on the outside of the absolute value symbol? – If the constant is positive, the graph moves up that many spaces. – If the constant is negative, the graph moves down that many spaces. • What happens when a constant is added on the inside of the absolute value symbol? – If the constant is positive, the graph moves to the left that many spaces. – If the constant is negative, the graph moves to the right that many spaces. Let’s use this knowledge and try a few more… Domain: Range: Domain: Range: Piecewise Functions • A piecewise function is a function that is written using two or more expressions. • The function is broken up into multiple pieces on a graph. • I know you are eager, so let’s look at one of these. Domain: {all real numbers} Range: {𝑦 𝑦 < −2 or 𝑦 = 1} Graph the piecewise function. Identify the domain and range. Domain: {all real numbers} Range: {all real numbers} You try. Graph the piecewise function. Identify the domain and range. Domain: {all real numbers} Range: {𝑦 𝑦 ≤ 2} • The cost of the postage to mail a letter is a function of the weight of the letter. But the function is not linear. It is a special function called a step function. • The graph of a step function consists of line segments or rays. Greatest Integer Function Graph each step function. Identify the domain and range. a) Domain: Range: b) Domain: Range: c) Domain: Range: • To recap: