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Library of Functions, Piecewise-Defined Functions

Library of Functions, Piecewise-Defined Functions. A linear function is a function of the form. f ( x ) =mx+b. The graph of a linear function is a line with a slope m and y- intercept b. Domain: All reals Range: All reals. ( 0,b ). A constant function is a function of the form.

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Library of Functions, Piecewise-Defined Functions

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  1. Library of Functions, Piecewise-Defined Functions

  2. A linear function is a function of the form f(x)=mx+b The graph of a linear function is a line with a slope m and y-intercept b. Domain: All reals Range: All reals (0,b)

  3. A constant function is a function of the form f(x)=b Domain: All reals Range: f(x) = b y b x

  4. Identity function is a function of a form: f(x)=x Domain: All reals Range: All reals (1,1) (0,0)

  5. The square function Domain: All reals Range: y ≥ 0

  6. Cube Function Domain: All reals Range: All reals

  7. Square Root Function Domain: All reals Range: y ≥ 0

  8. Reciprocal Function Domain: x ≠ 0 Range: y ≠ 0

  9. Absolute Value Function Domain: All reals Range: y ≥ 0 f(x) = |x|

  10. When functions are defined by more than one equation, they are called piece-wise defined functions.

  11. For the following function f(-1) = 2 a) Find f(-1) b) Find f(1) f(1) = 3 f(3) = 0 c) Find f(3)

  12. For the following function d)Sketch the graph.

  13. For the following function e) Find the domain.

  14. For the following function f(0) = 1 a) Find f(0) b) Find f(1) f(1) = 2 f(2) = 4 c) Find f(2)

  15. d)Sketch the graph. For the following function

  16. e) Domain. For the following function • Domain is [ -1 , ∞)

  17. In May of 2013 , Commonwealth Edison Company supplied electricity to residences for a monthly customer charge of $7.13 plus 8.27¢ per kilowatt hour (kWhr) for the first 400kWhr supplied in the month and 6.208¢ per kWhr for all usage over 400 kWhr in the month. A. What is the charge for using 300 kWhr in a month?B. What is the charge for using 700 kWhr in a month?C. If C is the monthly charge for x kWhr, express C as a function of x.

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