Grade 11 math

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1.Transform the graph of f(x) = 3^x to sketch g(x) = 3^-(x+1) -2. Show table of values and each transformation clearly to get full marks.

2.Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y = 3. Investigate whether other exponential functions have the same properties. Use the transformations to explain your observations.

I really appreciate your help! Thank you

  • Grade 11 math -

    1.

    - Reflection in the y - axis, since - f(x)
    - Left 2 units
    - Taken to the power of -2 (i forgot what they called this, i think you should look up this)


    2. Is there any vertical asymptote that you have to include in this function

  • Grade 11 math -

    2. If there's no vertical asympotote, then

    y = 3x^2 + 5 / x^2

    This way, for the denominator it shows there is no vertical asymptote. But when you plug in x = 0 for the numerator it equals 5 as the y-intercept. And since the numerator and denominator both have X^2 then this equals 3 / 1 = 3

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