Graph and state the domain & range, increasing/decreasing, asymptotes, and x & y intercepts

1. \(y=2^x\)

• Domain: \((-\infty,\infty)\)
• Range: \((0,\infty)\)
• Increasing
• Asymptote: \(x=0\)
• No x-intercept
• y-intercept: \((0, 1)\)
• 

2. \(y=\log_2x\)

• Domain: \((0,\infty)\)
• Range: \((-\infty,\infty)\)
• Increasing
• Asymptote: \(y=0\)
• x-intercept: \((1, 0)\)
• y-intercept: none
• 

3. \(y=e^x\)

• Domain: \((-\infty,\infty)\)
• Range: \((0,\infty)\)
• Increasing
• Asymptote: \(y=0\)
• No x-intercept
• y-intercept: \((0, 1)\)
• 

4. \(y=\ln x\)

• Domain: \((0,\infty)\)
• Range: \((-\infty,\infty)\)
• Increasing
• Asymptote: \(x=0\)
• x-intercept: \((1,0)\)
• y-intercept: NA
• 

5. \(y=-\ln(x+3)\)

• Domain: \((-3, \infty)\)
• Range: \((-\infty,\infty)\)
• Decreasing
• Asymptote: \(x=-3\)
• x-intercept: \((-2, 0)\)
• y-intercept: \(0, -\ln 2\)
• 

Simplify

6. \(e^{\ln4x}\)

• \(4x\)

7. \(e^{2ln4}\)

• \(16\)

8. \(8^{5\log_810}\)

• 100,000

9. \(10^{\log7}\)

• 7

10. \(10^{2\log7}\)

• 49

Expand

11. \(\log_2\sqrt[3]{\frac{M^2N}{2}}\)

• \(\frac{2}{3}\log_2M + \frac{1}{3}\log_2N -\frac{1}{3}\)

12. \(\log_2\frac{M}{N^2}\)

• \(\frac{1}{2}log_2N\)

13. \(\log_2(MN)^5\)

• \(5\log_2M+5\log_2N\)

14. \(\log_2M^5N^4\)

• \(5\log_2M+4\log_2N\)

Solve

15. \(\ln(x-1)+\ln(x+2)=\ln2+\ln(4-x)\)

• \(x=2\)

16. \(\log_2x=\frac{3}{2}\log_29+\log_22\)

• \(x=54\)

17. \(\log_3(x+2)+\log_36=3\)

• \(x=\frac{5}{2}\)

18. \(\log_8(3x-5) - \log_8(x-5)=\log_88\)

• \(x=7\)

19. \(2\log_3x-\log_3(x-2)=2\)

• \(x={3,6}\)

20. \(\log_4\frac{1}{16}=x\)

• \(x=-2\)

21. \(\log_2\sqrt[5]{16}=x\)

• \(x=\frac{4}{5}\)

22. \(2\log_b(2y+2)=\log_b16+2\log_b(y-2)\)

• \(y=5\)

23. \(e^{2x}-10e^x-11=0\)

• \(x=\ln 11\)

Notice that these answers are not “calculator answers”. Please leave your answers in this format for the quiz