y=3(2)^x what is the y intercept the x intercept and is the graph increasing or decreasing

Question

y=3(2)^x what is the y intercept the x intercept and is the graph increasing or decreasing

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Mary 2 weeks 2021-09-12T10:59:23+00:00 2 Answers 0

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    0
    2021-09-12T11:01:01+00:00

    This is an exponential function, with base 2. Since 2 is greater than 1, the function is increasing.

    For the y intercept, we have to set x=0, and we have

    y=3\cdot 2^0=3\cdot 1=3

    For the x intercept, we have to set y=0 and solve for x:

    3\cdot 2^x=0\iff 2^x=0

    And this has no solution. All we can say is that

    \displaystyle \lim_{x\to-\infty}2^x=0

    So, the x axis is an asymptote for the function, but the graph neves crosses it.

    0
    2021-09-12T11:01:06+00:00

    Answer:

    y-intercept: (0, 3)

    x-intercept: There isn’t one

    The graph is increasing.

    Step-by-step explanation:

    To find the y-intercept of a function, simply substitute 0 in for x, and calculate.

    To find the x-intercept of a function, simply substitute 0 in for y, and solve for x.

    To know whether the graph is increasing or decreasing, you need to look at what happens to the y-values as the value of x increases. If the values get bigger, it’s increasing and if they get smaller it’s decreasing.

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