1 p(x) = 2^x - 8 is an exponential equation. 2.1.1 Calculate the x - intercept of p. 2.1.2 The y-intercept of p. 2.1.3 The asymptote(s) of p. 2.1.4 Draw a neat sketch of the graph of p.

$$2^x = 2^3$$ $$x = 3$$

The $x$-intercept is $\boxed{(3, 0)}$.

2.1.2 The $y-$ intercept of $p$

$$p(0) = 1 - 8$$ $$p(0) = -7$$

The $y$-intercept is $\boxed{(0, -7)}$.

2.1.3 The asymptote(s) of $p$

In $p(x) = 2^x - 8$, the constant term is $-8$.
The horizontal asymptote is $\boxed{y = -8}$.

2.1.4 Draw a neat sketch of the graph of $p$
Since I cannot draw a graph directly, here are the key features for a neat sketch:

• The graph is an increasing exponential function.
• It passes through the $x$-intercept at $(3, 0)$.
• It passes through the $y$-intercept at $(0, -7)$.
• It has a horizontal asymptote at $y = -8$.
• The graph approaches $y = -8$ as $x$ approaches $-\infty$ and increases without bound as $x$ approaches $\infty$.