2.10 Solving equations graphically and analytically Quiz

1. Solve $e^{2x} - 3e^{x} + 2 = 0$.

• A. $x = 1$ or $x = 2$
• B. $x = 0$ or $x = \ln 2$
• C. $x = \ln 2$ only
• D. $x = e$ or $x = e^{2}$

2. Which substitution is most useful for $25^{x} - 6 \times 5^{x} + 5 = 0$?

• A. $u = 25^{x}$
• B. $u = x^{5}$
• C. $u = 6^{x}$
• D. $u = 5^{x}$

3. How many real solutions does $e^{2x} + e^{x} - 2 = 0$ have?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

4. A GDC shows the graphs of $y = f(x)$ and $y = g(x)$ meeting at $(0.52, 1.68)$. Which is a solution of $f(x) = g(x)$?

• A. $x = 0.52$
• B. $x = 1.68$
• C. $x = 2.20$
• D. $x = 1.16$

5. Two graphs intersect at $x = -1$ and $x = 3$, and $f(x) > g(x)$ at $x = 0$. For which $x$ is $f(x) > g(x)$ (assuming no other intersections)?

• A. $x < -1$ or $x > 3$
• B. $x > 3$
• C. $-1 < x < 3$
• D. $x < -1$