What are the domain, range, and asymptote of h(x) = (0.5)x – 9

Question

What are the domain, range, and asymptote of h(x) = (0.5)x – 9

in progress 0
2022-05-24T17:11:34+00:00 2 Answers 0

Answers ( 2 )

  1. Adalyn
    0
    2022-05-24T17:13:15+00:00

    Answer:

    The domain of h(x) is {x : x is a real number}

    The range of the function is {y : y > -9}

    The horizontal asymptote is at y = -9

  2. Emery
    0
    2022-05-24T17:13:28+00:00

    Answer:

    The domain of h(x) is {x : x u2208 R}

    The range of the function is {y : y > -9}

    The horizontal asymptote is at y = -9

    Step-by-step explanation:

    * Lets read the problem and solve it

    – The exponential function is f(x) = a(b)^x, where a and b are constant

    and b is the base , x is the exponent , a is the initial value of f(x)

    – The domain of the function is all the values of x which make the

    function defined

    – The range of the function is the set of values of y that corresponding

    with the domain x

    – Asymptote on the graph a line which is approached by a curve but

    never reached

    – A function of the form f(x) = a(b^x) + c always has a horizontal

    asymptote at y = c

    * Lets solve the problem

    u2235 h(x) = (0.5)^x – 9

    u2235 All the values of x make h(x) defined

    u2235 The domain of the function is the values of x

    u2234 The domain of h(x) is {x : x u2208 R} u21d2 R is the set of real number

    u2235 The range of the function is the set of values of y which

    corresponding to x

    u2235 (0.5)^x must be positive because there is no values of x make it

    negative value

    u2234 y must be greater than -9

    u2234 The range of the function is {y : y > -9}

    u2235 A function of the form f(x) = a (bx) + c always has a horizontal

    asymptote at y = c

    u2235 h(x) = (0.5)^x – 9

    u2234 c = -9

    u2234 The horizontal asymptote is at y = -9

    * Look to the attached file for more understanding

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