Mathematics

Question

Which statements are true for the functions g(x) = x2 and h(x) = -x2? Check all that apply.

2 Answer

  • ANSWER

    See below

    EXPLANATION

    The given functions are:

    [tex]g(x) = {x}^{2} [/tex]

    and

    [tex]h(x) = - {x}^{2} [/tex]

    The following statements are true;

    h(x) is the reflection of g(x) in the x-axis.

    g(x) opens upwards while h(x) opens downwards

    Both functions have their vertex and intercepts at the origin.

    The x-axis is a tangent to both functions at x=0.

    g(x) has a minimum point

    h(x) has a maximum point.

  • Answer:

    For any value of x, g(x) will always be greater than h(x).

    For any value of x, h(x) will always be greater than g(x).

    g(x) > h(x) for x = -1. TRUE

    g(x) < h(x) for x = 3.

    For positive values of x, g(x) > h(x). TRUE

    For negative values of x, g(x) > h(x). TRUE

    Step-by-step explanation:

    answer on edge

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