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Evaluating Functions Tutorial

Evaluating Functions Tutorial. When we evaluate a function we are finding the function value for a specific input. To do this we replace the function variable in the function’s formula with the specific input and proceed from there.

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Evaluating Functions Tutorial

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  1. Evaluating FunctionsTutorial

  2. When we evaluate a function we are finding the function value for a specific input. To do this we replace the function variable in the function’s formula with the specific input and proceed from there. The “specific input” can be a constant, another variable or an algebraic expression. The important thing to remember is it replaces the function variable everywhere in the function’s formula For example:

  3. Another example:

  4. Another example: Because 5/0 is undefined 4 is not in the domain of h(x).

  5. Another example: Because is an imaginary number 1 is not in the domain of f (x)

  6. Problems - 1 Given find

  7. Problems - 2

  8. Sometimes a function has different rules or formulas depending on what the input value is. These functions are known as piece-wise definedfunctions.

  9. Problems - 3

  10. The Difference Quotient The difference quotientof a function f (x) is defined as follows: This is used in calculus when finding derivatives so it is worthwhile to become familiar with it in precalculus.

  11. Find the difference quotients for the following functions:

  12. The difference quotient for

  13. The difference quotient for

  14. The difference quotient for

  15. Problems - 4 Find the difference quotient for the following function (click on mouse to see answer).

  16. Problems - 5 Find the difference quotient for the following function (click on mouse to see answer).

  17. Problems - 6 Find the difference quotient for the following function (click on mouse to see answer).

  18. Average Rate of Change A special kind of difference quotient is the average rate of change.We can use the function values at two different points, a and b to find the average rate of change of a function over the interval [ a, b ]. This is given by: Notice, this is equal to the slope of the line connecting the two points ( a, f(a) ) and ( b, f(b) ). The average rate of change for the function f (x) = x2 over the interval [2,4] is:

  19. Find the average rate of change for each of the following functions over the given intervals (click on mouse to see answer).

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