The image you uploaded contains an exercise that asks you to:

1. Graph the given functions using a graphing calculator, and sketch the graphs.
2. Draw secant lines on your sketch to estimate the slope of the tangent line at $x = 2$.
3. Calculate and record the slopes of these secant lines, then use them to estimate the slope of the tangent line at $x = 2$.

The functions provided in the exercise are:

• (a) $f(x) = 3x^2 - 5x + 1$
• (b) $f(x) = 3^x + 1$
• (c) $f(x) = \sqrt{x + 2}$
• (d) $f(x) = 2x - 7$

Key Steps:

1. Use a graphing calculator to plot each function.
2. Draw secant lines (lines that connect two points on the graph).
3. Find the slope of the secant lines around $x = 2$ (e.g., between $x = 1.5$ and $x = 2.5$).
4. Use the secant slopes to estimate the slope of the tangent line at $x = 2$.

Let me know if you'd like more detailed help with graphing any of these functions or finding the slopes of secant lines!

Here are five related questions:

1. What is the definition of a secant line in calculus?
2. How is the tangent line at a point related to the secant line?
3. How can you estimate the slope of the tangent line from secant lines?
4. What is the derivative of $f(x) = 3x^2 - 5x + 1$?
5. How do the slopes of secant lines approach the slope of the tangent line as the two points get closer?

Tip: The slope of a secant line between two points $(x_1, f(x_1))$ and $(x_2, f(x_2))$ is given by the difference quotient:
$m_{\text{secant}} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$