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anonymous

  • one year ago

A function is shown in the table. x g(x) −2 2 −1 −3 0 2 1 17 Which of the following is a true statement for this function? The function is increasing from x = −2 to x = −1. The function is increasing from x = 0 to x = 1. The function is decreasing from x = −1 to x = 0. The function is decreasing from x = 0 to x = 1.

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  1. anonymous
    • one year ago
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    Hi @kkailyn This problem seems relatively straightforward. Where exactly are you getting stuck?

  2. anonymous
    • one year ago
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    Im kind of confused on how to actually answer it. @Nengeni

  3. anonymous
    • one year ago
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    oh nevermind its c. @Nengeni

  4. anonymous
    • one year ago
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    @kkailyn C is actually the incorrect answer. As you can see from your chart, at x = (-1), the function is at -3, and at x = (0), the function is at 2. Since the function is going from -3 to 2, the function is actually increasing between x = (-1) and x = (0).

  5. anonymous
    • one year ago
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    then it has to be B

  6. anonymous
    • one year ago
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    @Nengeni

  7. anonymous
    • one year ago
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    @kkailyn That is correct!

  8. anonymous
    • one year ago
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    would you mind helping me with two more? @Nengeni

  9. anonymous
    • one year ago
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    @kkailyn Not at all!

  10. anonymous
    • one year ago
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    ok well this one i already have answered it but im not quite sure im right. Two quadratic functions are shown. Function 1: f(x) = 2x2 − 8x + 1 Function 2: x g(x) −2 2 −1 −3 0 2 1 17 Which function has the least minimum value and what are its coordinates? Function 1 has the least minimum value and its coordinates are (0, 1). Function 1 has the least minimum value and its coordinates are (2, −7). Function 2 has the least minimum value and its coordinates are (0, 2). Function 2 has the least minimum value and its coordinates are (−1, −3).

  11. anonymous
    • one year ago
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    @Nengeni

  12. anonymous
    • one year ago
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    @kkailyn What do you think the answer is for this question?

  13. anonymous
    • one year ago
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    @nengeni B. The last guy that helped me kind of confused me.

  14. anonymous
    • one year ago
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    B is the correct answer.

  15. anonymous
    • one year ago
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    ok now the last one. The function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

  16. anonymous
    • one year ago
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    You can see from the chart that function #2 has a minimum value of (-1,-3). We know this because the x values on either side of -1, -2 and 0, provide us with y values that are greater than -3. Now that we know what the minimum value is for function #2, we need to find the minimum for function #1. We can do this by using the first bit of the quadratic formula (-b/2a). Plugging in function #1 gives us (8/4) or 2. This represents the x value of the vertex. Plugging 2 into function #1 gives us an answer of -7, or a vertex of (2,-7). Now that we know both vertices, we can see that, since -7 is smaller than -3, function #1 has the least minimum value, occurring at (2,-7)

  17. anonymous
    • one year ago
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    Not sure if I asked before... are you familiar with the quadratic formula?

  18. anonymous
    • one year ago
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    Yes that is what the other person said but he confused me. And ive done it before just not well at it. @Nengeni

  19. anonymous
    • one year ago
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    Since you know the quadratic formula, the first part is relatively simple. Once again, using the first bit of the quadratic formula (-b/2a) we can find the x value of the vertex. Let's do that... (-50/-2) = 25. This is the x value so let's plug it into the equation and find the corresponding y value. f(25) = -25^2 + 50*25 - 264 = 625 + 1250 - 264 = 1611. The vertex can be found at (25,1611)

  20. anonymous
    • one year ago
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    In this equation, the vertex represents the maximum profit, which will be found when 25 memberships are sold.

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