Linear Functions, Their Properties, and Linear Models

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Presentation transcript:

Linear Functions, Their Properties, and Linear Models Section 4.1 Linear Functions, Their Properties, and Linear Models

OBJECTIVE 1

Graph the linear function What is the domain and the range of f? …

OBJECTIVE 2

.12 - .09 = .03 1 -0 .16 - .12 = .04 2 - 1 .22 - .16 = .06 3 - 2

37.5 – 40 = -.25 70 - 60 47.5 - 50 = 30 - 20 45 – 47.5 = 40 - 30 42.5 – 45 = 50 - 40 40 – 42.5 = 60 - 50

OBJECTIVE 3

Determine whether the following linear functions are increasing, decreasing, or constant. …

OBJECTIVE 4

What is the implied domain of the function found in part (a)? Suppose that a company just purchased some new office equipment at a cost of $2500 per machine. The company chooses to depreciate each machine using the straight-line method over 5 years. Build a linear model that expresses the value V of each machine as a function of its age, x. What is the implied domain of the function found in part (a)? Graph the linear function. What is the value of each machine after 2 years? Interpret the slope. When will the value of each machine be $500? (a) V(x) = -500x + 2500 (b) 0 ≤ x ≤ 5 (d) V(2) = -500(2) + 2500 = 1500 (e) Rate at which machine depreciates (f) After 4 years: V(4) = -500(4) + 2500 = 500