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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