Question

a baseball is hit into the air. its height in feet after t seconds is modeled by ( h(t) = 64t - 16t^2 ).
which statement best describes the domain of ( h(t) )?
a. the domain is 0,4 because the ball hits the ground after 4 seconds.
b. the domain is 24,64 because the ball reaches 64 feet.
c. the domain is 0,16 because the ball travels for 16 seconds.
d. the domain is 3,8 because the ball remains in the air for 8 seconds.
16.
select three of the values that are in the domain of the function represented by the graph.
graph of a parabola opening downward, with x-intercepts at -3 and 4, vertex between them
a. 3
b. -1
c. 5
d. 0
e. -4

Explanation:

Question 1 (about the domain of \( h(t) = 64t - 16t^2 \))

Step 1: Find when the ball hits the ground

To find when the ball hits the ground, set \( h(t) = 0 \):
\( 64t - 16t^2 = 0 \)
Factor out \( 16t \): \( 16t(4 - t) = 0 \)
This gives solutions \( t = 0 \) (when the ball is hit) and \( t = 4 \) (when the ball hits the ground).

Step 2: Determine the domain

Time \( t \) cannot be negative in this context (since we start timing when the ball is hit). So \( t \) ranges from \( 0 \) to \( 4 \), meaning the domain is \( [0, 4] \).

The graph is a parabola opening downward, with \( x \)-intercepts (where the graph touches the \( x \)-axis) at \( x = -3 \) (or similar left intercept) and \( x = 4 \) (right intercept). The domain is the set of \( x \)-values the graph covers, which appears to be from \( -3 \) to \( 4 \) (or similar, based on the graph).

• Check each option:
• \( a. 3 \): Between the intercepts (if domain is \([-3, 4]\) or similar), so in domain.
• \( b. -1 \): Between the intercepts, so in domain.
• \( c. 5 \): Greater than the right intercept (e.g., 4), so not in domain.
• \( d. 0 \): Between the intercepts, so in domain.
• \( e. -4 \): Less than the left intercept (e.g., -3), so not in domain.

So the three values in the domain are \( 3 \), \( -1 \), and \( 0 \).

Answer:

A. The domain is \([0,4]\) because the ball hits the ground after 4 seconds.

Question 16 (select three values in the domain of the graph)