Question

according to the graph of h(w) below, what happens when the width approaches zero?
a. the height gets very large
b. the height gets very small.
c. the height approaches a horizontal asymptote.
d. the height equals zero.

Explanation:

Step1: Analyze the graph's behavior near w=0

The graph of \( H(w) \) (height vs. width) shows that as the width \( w \) approaches 0 (from the right, since width is a positive quantity), the height values are near the y - axis (where \( w = 0 \)) and the curve is rising steeply.

Step2: Evaluate each option

• Option A: As \( w

ightarrow0 \), looking at the graph (the curve near \( w = 0 \) is going up towards large values of height), so the height gets very large.

• Option B: The graph is increasing near \( w = 0 \), so height does not get very small.
• Option C: A horizontal asymptote is approached as \( w

ightarrow\infty \) (the curve flattens out towards the x - axis as \( w \) becomes large), not as \( w
ightarrow0 \).

• Option D: The height does not equal zero when \( w

ightarrow0 \), the curve is far from \( y = 0 \) near \( w = 0 \).

Answer:

A. The height gets very large