4.5E: Graphs of Logarithmic Functions (Exercises)

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section 4.5 exercise

For each function, find the domain and the vertical asymptote.

1. $f\left(x\right)=\log \left(x-5\right)$

2. $f\left(x\right)=\log \left(x+2\right)$

3. $f\left(x\right)=\ln \left(3-x\right)$

4. $f\left(x\right)=\ln \left(5-x\right)$

5. $f\left(x\right)=\log \left(3x+1\right)$

6. $f\left(x\right)=\log \left(2x+5\right)$

7. $f\left(x\right)=3\log \left(-x\right)+2$

8. $f\left(x\right)=2\log \left(-x\right)+1$

Sketch a graph of each pair of functions.

9. $f\left(x\right)=\log \left(x\right),\; g\left(x\right)=\ln \left(x\right)$