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Jane threw a basketball up in the air. The following table represents the height [tex]\( f(t) \)[/tex], in meters, of the ball above the ground at time [tex]\( t \)[/tex] seconds:

[tex]\[
\begin{tabular}{|c|c|}
\hline
Time \( (t) \) (in seconds) & Height \( f(t) \) (in meters) \\
\hline
2 & 10 \\
\hline
4 & 15 \\
\hline
6 & 10 \\
\hline
8 & 0 \\
\hline
\end{tabular}
\][/tex]

Which of the following is represented by the [tex]\( x \)[/tex]-intercept of [tex]\( f(t) \)[/tex]?

A. The ball reaches the maximum height in 4 seconds.
B. The ball reaches a maximum height of 15 meters.
C. The ball was thrown from a height of 10 meters.
D. The ball touches the ground after 8 seconds.

Sagot :

GinnyAnsweridn
To determine what the [tex]$x$[/tex]-intercept of [tex]$f(t)$[/tex] represents, let's analyze the provided table of the height of the ball over time:

[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Height $f(t)$ \\ \hline 2 & 10 \\ \hline 4 & 15 \\ \hline 6 & 10 \\ \hline 8 & 0 \\ \hline \end{tabular} \][/tex]

The [tex]$x$[/tex]-intercept is the point where the function [tex]$f(t)$[/tex] crosses the [tex]$x$[/tex]-axis, which is when the height [tex]$f(t) = 0$[/tex]. This represents the time [tex]\( t \)[/tex] at which the ball touches the ground. From the provided table:

- At [tex]\( t = 2 \)[/tex] seconds, the height [tex]\( f(t) \)[/tex] is 10 meters.
- At [tex]\( t = 4 \)[/tex] seconds, the height [tex]\( f(t) \)[/tex] is 15 meters.
- At [tex]\( t = 6 \)[/tex] seconds, the height [tex]\( f(t) \)[/tex] is 10 meters.
- At [tex]\( t = 8 \)[/tex] seconds, the height [tex]\( f(t) \)[/tex] is 0 meters.

From this data, we observe that the ball touches the ground at [tex]\( t = 8 \)[/tex] seconds.

Therefore, the [tex]$x$[/tex]-intercept of [tex]$f(t)$[/tex] represents the time when the ball touches the ground. Hence, the correct option is:

The ball touches the ground after 8 seconds.
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