College Algebra, 4th Edition

Review Exercises

Concepts and Vocabulary

In Exercises 1–10, state whether the given statement is true or false.

1. The function $f(x)=a^x$ is exponential if $a>0.$

2. The graph of $f(x)=4^x$ approaches the x-axis as $x\to -\infty .$

3. The domain of $f(x)=\log (2-x)$ is $(-\infty ,2].$

4. The equation $u={10}^v$ means that $\log u=v.$

5. The inverse of $f(x)=\ln x$ is $g(x)=e^x.$

6. The graph of $y=a^x(a>0,a\ne 1)$ always contains the points (0, 1) and (1, a).

7. $\ln (M+N)=\ln M+\ln N$

8. $\log \sqrt{300}=1+{\displaystyle \frac{1}{2}}\log 3$

9. The functions $f(x)=2^{-x}$ and $g(x)={\left({\displaystyle \frac{1}{2}}\right)}^x$ have the same graph.

10. $\ln u={\displaystyle \frac{\log u}{\log e}}$

Building Skills

In Exercises 11–18, match the function with its graph in (a)–(h).

1. 11. $f_1(x)={\log }_{2}x$

   12. $f_2(x)=2^x$

   13. $f_3(x)={\log }_2(3-x)$

   14. $f_4(x)={\log }_{1/2}(x-1)$

   15. $f_5(x)=-{\log }_{2}x$

   16. $f_6(x)={\left({\displaystyle \frac{1}{2}}\right)}^x$

   17. $f_7(x)=3-2^{-x}$

   18. $f_8(x)={\displaystyle \frac{6}{1+2e^{-x}}}$

In Exercises ...