Rational Function
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An asymptote is an imaginary line that a graph approaches but never touches as it goes to infinity. The document provides examples of graphs with rational functions that have vertical and horizontal asymptotes. It also discusses the square root function and how it is the inverse of the quadratic function. The square root function is only defined for non-negative inputs. Changing the parameters a and b in the square root function changes the shape and orientation of the graph.
Rational Function
- 2. What is an asymptote? • An asymptote is an imaginary line being approached but never touched or intersected by a graph as it goes through infinity.
- 3. Example 1: Sketch the graph of a rational function g( x) = V. A : x = 2 H. A : y = 0 g (0) = - 3/2 g (3) = 3 3 x−2
- 4. Example 2: Sketch the graph of f ( x) = V. A : x = 2, x = -1 H. A : y = 0 f(-2) = - 1/2 f(0) = 0 f(1) = - 1/2 f(3) = 3/4 x x2 − x − 2
- 6. The square root function is actually the inverse operation of the quadratic function. f (x ) = x x 0 1 4 9 f(x)
- 7. The square root function is actually the inverse operation of the quadratic function. f (x ) = x x 0 1 4 9 f(x) 0
- 8. The square root function is actually the inverse operation of the quadratic function. f (x ) = x x 0 f(x) 0 1 1 4 9
- 9. The square root function is actually the inverse operation of the quadratic function. f (x ) = x x 0 f(x) 0 1 1 4 2 9
- 10. The square root function is actually the inverse operation of the quadratic function. f (x ) = x x 0 f(x) 0 1 1 4 2 9 3
- 11. The square root function is actually the inverse operation of the quadratic function. f (x ) = x f (x ) = − x x 0 f(x) 0 x 0 1 1 1 4 2 4 9 3 9 f(x)
- 12. The square root function is actually the inverse operation of the quadratic function. f (x ) = x f (x ) = − x x 0 f(x) 0 x 0 1 1 1 4 2 4 9 3 9 f(x) 0
- 13. The square root function is actually the inverse operation of the quadratic function. f (x ) = x f (x ) = − x x 0 f(x) 0 x 0 f(x) 0 1 1 1 -1 4 2 4 9 3 9
- 14. The square root function is actually the inverse operation of the quadratic function. f (x ) = x f (x ) = − x x 0 f(x) 0 x 0 f(x) 0 1 1 1 -1 4 2 4 -2 9 3 9
- 15. The square root function is actually the inverse operation of the quadratic function. f (x ) = x f (x ) = − x x 0 f(x) 0 x 0 f(x) 0 1 1 1 -1 4 2 4 -2 9 3 9 -3
- 16. Remember that it is not possible to get the square root of a negative number, therefore the values that are chosen for x in the table of values must be strategic. − = Error f (x ) = x x 0 1 2 3 f(x) 0 1 1.4 2.8 f (x ) = x x 0 -1 -4 -9 f(x) 0 Error Error Error It is possible however, to use non-perfect squares with this function. You will end uo with an irrational y-value that needs to be rounded off but that’s okay. It just makes it a little more awkward to plot on the graph.
- 17. If we play with parameter ‘a’, we can see its effect on the resulting graph. f (x ) = 2 x a = 2 a = 1 f (x ) = x f (x ) = 1 x; 2 a = 1 2 f (x ) = − x a = -1
- 18. If we play with parameter ‘b’, we can see its effect on the resulting graph. f (x ) = 2x b = 2 a = 1 f (x ) = x 1 f (x ) = x; 2 1 b= 2 f (x ) = − x b = -1
- 19. The signs of parameters a and b determine which way the square root function moves from its vertex. f (x ) = − x a = -; b = + a = +; b = + f (x ) = x f (x ) = − x a = +; b = - f (x ) = − − x a = -; b = -
- 20. THANK YOU !!! ---Ms. Jerlyn Fernandez