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Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
Basics of functions continued
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Basics of functions continued

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  • 1. Basics of Functions Continued… <ul><li>Domain </li></ul><ul><li>Evaluating from… </li></ul><ul><ul><li>An equation </li></ul></ul><ul><ul><li>A graph </li></ul></ul><ul><ul><li>A table </li></ul></ul><ul><li>Composition </li></ul><ul><ul><li>Add/Subtract/Multiply/Divide </li></ul></ul><ul><ul><li>Difference Ratio </li></ul></ul>
  • 2. Domain
  • 3.  
  • 4.  
  • 5.  
  • 6.  
  • 7.  
  • 8.  
  • 9. <ul><li>6. Given the graph, if possible, evaluate (f + g)(1). </li></ul><ul><li>f(1) = (think when x = 1 on the f(x) graph, what is the y-value?) </li></ul><ul><li>g(1) = (think when x = 1 on the g(x) graph, what is the y-value?) </li></ul><ul><li>(f + g)(1) = add the two parts above together </li></ul>– 4 – 2 2 5 0 9 4 a. x y
  • 10. <ul><li>6. Given the graph, evaluate (f + g)(1). </li></ul><ul><li>f(1) = 3 g(1) = 1 </li></ul><ul><li>(f + g)(1) = 4 </li></ul>– 4 – 2 2 5 0 9 4 a. x y
  • 11. <ul><li>7. Given the graph, if possible, evaluate (f / g)(0). </li></ul><ul><li>f(0) = (think when x = 0 on the f(x) graph, what is the y-value?) </li></ul><ul><li>g(0) = (think when x = 1 on the g(x) graph, what is the y-value?) </li></ul><ul><li>(f / g)(0) = divide </li></ul>– 4 – 2 2 5 0 9 4 x y
  • 12. <ul><li>7. Given the graph, evaluate (f / g)(0). </li></ul><ul><li>f(0) = 1 </li></ul><ul><li>g(0) = 0 </li></ul><ul><li>(f /g)(0) = 1/0, thus (f/g)(0) is undefined because the denominator </li></ul><ul><li>is 0. </li></ul>– 4 – 2 2 5 0 9 4 x y
  • 13. <ul><li>8. Given the table, if possible, use the given representations of f and g to evaluate (f · g)(1). </li></ul><ul><li>f(1), when x = 1 in the table, what is the value of f(x)? </li></ul><ul><li>g(1), when x = 1 in the table, </li></ul><ul><li>what is the value of g(x)? </li></ul><ul><li>(f · g)(1), evaluate the product </li></ul>x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2
  • 14. <ul><li>8. Given the table, if possible, use the given representations of f and g to evaluate (f · g)(1). </li></ul><ul><li>f(1) = 3 </li></ul><ul><li>g(1) = 1 </li></ul><ul><li>(f · g)(1) = 3(1) </li></ul><ul><li>= 3 </li></ul>x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2
  • 15. <ul><li>9. Given the table, if possible, use the given representations of f and g to evaluate (f – g)(-2). </li></ul><ul><li>f(-2), when x =-2 in the table, what is the value of f(x)? </li></ul><ul><li>g(-2), when x = -2 in the table, </li></ul><ul><li>what is the value of g(x)? </li></ul><ul><li>(f – g)(-2), evaluate the difference </li></ul>x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2
  • 16. <ul><li>9. Given the table, if possible, use the given representations of f and g to evaluate (f – g)(-2). </li></ul><ul><li>f(-2) = -3 </li></ul><ul><li>g(-2) = undefined </li></ul><ul><li>(f – g)(-2) = undefined </li></ul><ul><li>Note: looking back at the graph on slide 7, g(x) is not </li></ul><ul><li>defined at x = -2. In simplistic </li></ul><ul><li>terms, that means there is no graph for the value of x. </li></ul>x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2

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