Algebra All exponential functions have as domain the set of real numbers because the domain is the set of numbers that can enter the function and enable to produce a number as output. In exponential functions whatever real number can be operated. (-infinity, infinity)

You have ln (x+4) so everything is shifted by 4. The domain of ln (x+4) is now -4 < x < infinity (Shifting infinity by a finite number gives you infinity again.) So,-4 < x < infinity is the domain of ln (x+4).

(2 [less than] t [less than] infinity)

For your function f (t) = 5.5exp (t) the function is continuous for all values of t as exp (t) is continuous for all values...

The domain of the function is -oo < t < oo
2a. subtracting 3 on the inside the function moves it 3 units to the right, that's the only transformation.

the vertical asymptote results from an invalid input to the function, like dividing by zero or taking the square root of a negative number, or in this case, taking the log of zero. so we need to find the value where x-3=0, thus the asymptote occurs at x=3. The x intercept is when y (or g (x) in this case)=0-0=g (x)=log (x-3) log (x-3)=0 x-3=10^0 x-3=1 x=4 so the intercept is at (4,0)

2b. We see that the right side of g (x), which is -log (x), is the result of multiplying the…