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Falling_In_Katt

  • one year ago

***WILL MEDAL*** You have two exponential functions. One has the formula h(x) = -2 x + 8. The other function, g(x), has the graph shown below. https://gordon.owschools.com/media/o_anageo_ccss_2014/8/alg1_9_20_34_exponential.gif Which inequality below is true on the indicated interval? A. g(x) ≥ h(x) on the interval -2 ≤ x ≤ -1 B. h(x) ≤ g(x) on the interval -1 ≤ x ≤ 0 C. g(x) ≥ h(x) on the interval 0 ≤ x ≤ 1 D. h(x) ≤ g(x) on the interval 1 ≤ x ≤ 2

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  1. Falling_In_Katt
    • one year ago
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    @ChillOut @mathstudent55 @Jadeishere @Elsa213 @welshfella @paki @ParthKohli @uri

  2. Falling_In_Katt
    • one year ago
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    @TheSmartOne

  3. ChillOut
    • one year ago
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    Is h(x) \(2^{x}+8\)?

  4. Falling_In_Katt
    • one year ago
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    i think so

  5. ChillOut
    • one year ago
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    Because it'll be completely different if it's \(2^{x+8}\)

  6. Falling_In_Katt
    • one year ago
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    i think its the first one

  7. ChillOut
    • one year ago
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    All right... So let's find g(x)'s equation. Since we know it is an exponential function, it has the following form: \(a^{x}+z\). For the first and easiest part, we can find z by simply making x=0. This gives z=3, which is the "y intercept".

  8. Falling_In_Katt
    • one year ago
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    My guess is D...?

  9. ChillOut
    • one year ago
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    Are you guessing or did ou try to finish it? xD

  10. ChillOut
    • one year ago
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    All right, moving on... So to find a, we just make x=1, so we have g(1)=a+3, and since we have the value of g(1), which is 6, we can do the following: \(6=a^{1}+3,a=3\). So we have \(g(x)=3^{x}+3,\)

  11. Falling_In_Katt
    • one year ago
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    This is just confusing me...

  12. ChillOut
    • one year ago
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    I'm just finding the equation for g(x). Now I can keep moving on the problem

  13. Falling_In_Katt
    • one year ago
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    okay

  14. ChillOut
    • one year ago
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    Oh god, I've found an major error. But all right, I'll redo, with the same steps.

  15. ChillOut
    • one year ago
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    g(x)=\(a^{x}+z\) g(0)=3, so 1+z= 3, z=2. g(1)=6, so a + 2=6 and a=4 We have \(g(x)=4^{x}+2\)

  16. ChillOut
    • one year ago
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    Now we test the options... Just plug in the values in the fuctions and check if the statements are true or false! Can you do that?

  17. Falling_In_Katt
    • one year ago
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    yes! thank you.

  18. ChillOut
    • one year ago
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    No problem!

  19. ChillOut
    • one year ago
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    I'm still here if you get stuck.

  20. Falling_In_Katt
    • one year ago
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    im still getting D

  21. ChillOut
    • one year ago
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    All right, let me check, one moment.

  22. ChillOut
    • one year ago
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    It seems you're right. g(1) = 6, f(1) = 6 g(2) = 18, f(2) = 4 So g(1)=f(1) and g(2)>f(2).

  23. Falling_In_Katt
    • one year ago
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    Okay thank you

  24. ChillOut
    • one year ago
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    No problem. If you need help, just ask.

  25. Falling_In_Katt
    • one year ago
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    okay

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