Question

I'm doing parent functions for calculus.
What are the domains and ranges for:
1. f(x)=a^x
2. f(x)=logaX
3. f(x)=sinX
4. f(x)=cosX
5. f(x)=tanX

Answer 1

1) all real numbers. you can raise a to any power
2)
\[(0,\infty)\] you cannot take the log of a negative number because
\[a^x=\text{something negative}\] has no solution

Answer 2

3) sine all real number

Answer 3

4) cosine all real numbers

Answer 4

5) tangent all numbers except those for which
\[\cos(x)=0\]
those would be numbers like
\[\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2}\] i.e. all real numbers except
\[x=\frac{(2k-1)\pi}{2}\] for integer k

Answer 5

Thanks a lot. but
for f(x)=logaX , what would the graph look like.