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Functions and Graphs

Functions and Graphs. Property of Texas Tech University Department of Mathematics & Statistics. Graphs. The graph of is the collection of all points. Vertical Line Test. A curve in the plane is the graph of a function if and only if it intersects vertical lines no more than once

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Functions and Graphs

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  1. Functions and Graphs Property of Texas Tech University Department of Mathematics & Statistics

  2. Graphs The graph of is the collection of all points

  3. Vertical Line Test A curve in the plane is the graph of a function if and only if it intersects vertical lines no more than once a function not a function

  4. Symmetry A function is called even if for all in the domain of . Symmetric with respect to the y-axis

  5. Symmetry A function is called odd if for all in the domain of . Symmetric with respect to the origin for all odd functions

  6. Symmetry

  7. Determine the symmetry of Solution is even: is odd: is not symmetric. Why?

  8. Be sure that you know the Directory of Curves in Table 1.4 identity: quadratic: cubic: absolute value:

  9. square root: cube root: reciprocal: reciprocal squared:

  10. tangent: secant:

  11. Classification of Functions Polynomials : degree of : leading coefficient : constant term

  12. If is another polynomial, say then if and only if and for all

  13. Classification of Functions Rational functions where and are polynomials For example

  14. Classification of Functions Algebraic functions are constructed from polynomials using the operations of -addition -subtraction -multiplication -division -rational power All other functions are called transcendental, for example: trigonometric, exponential, logarithmic

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