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  • [FREE] Describe the graph of the function at its roots. g(x) = (x + 4 . . .
    Behavior at x = − 4: Since (x + 4) 4 is raised to an even power, the graph will touch the x-axis at this point, indicating that there is a local minimum here, but it does not cross the x-axis Therefore, at x = − 4, the graph touches the x-axis Behavior at x = 9: The term (x − 9) is raised to the first power, which is odd This means
  • [FREE] g(x)=(x+4)^4(x-9) At x=-4, the graph [blank] the x-axis. At x=9 . . .
    An even exponent indicates that the graph will 'touch' the x-axis at this point without crossing it This means as the graph approaches x = − 4, it will come down to the x-axis, touch it, and then turn back in the same direction Conclusion: At x = − 4, the graph touches the x-axis At x = 9: The factor (x − 9) has an exponent of 1, which
  • [FREE] The graph of f(x) = x^2 was transformed to create the graph of g . . .
    When we transform f (x) into g (x) by subtracting 9 (i e , g (x) = x 2 − 9), we are effectively moving the entire graph downward This is known as a vertical shift This is known as a vertical shift
  • [FREE] How does the graph of f (x) = (x - 9)^4 - 3 compare to the . . .
    Horizontal Shift: The term (x − 9) indicates a horizontal shift Since it is (x − a) where a = 9, the graph of g (x) is shifted 9 units to the right This means all points on the graph of g (x) will now be located 9 units to the right Vertical Shift: The subtraction of 3 in − 3 moves the graph downward Therefore, the entire graph is





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