Question

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

Answer 1

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

Answer 2

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