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Given : \[ \begin{array}{l} f(x)=2 x+1 \\ g(x)=5 \times 2 \\ h(x)=x+3 \end{array} \] 1. \( (f \circ g)(x) \) 2. \( (g=f)(x) \) 3. \( (h \circ g)(x) \) 4. \( (f \circ h)(x) \) Finally, we are almost done with the preview of Functions! Some real life situations can also be represented by functions. Take a closer look at how some events are written as functio is! FUNCTIONS IN REAL-LIFE SITUATIONS 1) Suppose that s ( \( ( \) ) is the top speed (in km per hour) of a runner when the temperature is \( T \) degrees Celsius. Explain what the statements \( s(15)=12 \) and \( s(30) \) \( =10 \) mean. Solution: The first equation means that when the temperature is \( 15^{\circ} \mathrm{C} \), then the top speed of a runner is 12 km per hour. However, when temperature rises to \( 30^{\circ} \mathrm{C} \), the top speed is reduced to 10 km per hour. 2). The velocity \( V \) (in \( \mathrm{m} / \mathrm{s} \) ) of a ball thrown upward \( t \) seconds after the ball was thrown is given by \( V(t)=20-9.8 t \). Calculate \( V(0) \) and \( V(1) \), and explain what these results mean. Solution. \( V(0)=20-9.8(0)=20 \) and \( V(1)=20-9.8(1)=10.2 \). These results indicate that the initial velocity of the ball is \( 20 \mathrm{~m} / \mathrm{s} \). After 1 second, the ball is traveling more slowly, at \( 10.2 \mathrm{~m} / \mathrm{s} \). Do you want to try expressing real life situations as a function of an unknown variable? Answer Activity 6 below.

          Given :
\[
\begin{array}{l}
f(x)=2 x+1 \\
g(x)=5 \times 2 \\
h(x)=x+3
\end{array}
\]
1. \( (f \circ g)(x) \)
2. \( (g=f)(x) \)
3. \( (h \circ g)(x) \)
4. \( (f \circ h)(x) \)

Finally, we are almost done with the preview of Functions!
Some real life situations can also be represented by functions. Take a closer look at how some events are written as functio is!

FUNCTIONS IN REAL-LIFE SITUATIONS
1) Suppose that s ( \( ( \) ) is the top speed (in km per hour) of a runner when the temperature is \( T \) degrees Celsius. Explain what the statements \( s(15)=12 \) and \( s(30) \) \( =10 \) mean.
Solution:
The first equation means that when the temperature is \( 15^{\circ} \mathrm{C} \), then the top speed of a runner is 12 km per hour. However, when temperature rises to \( 30^{\circ} \mathrm{C} \), the top speed is reduced to 10 km per hour.
2). The velocity \( V \) (in \( \mathrm{m} / \mathrm{s} \) ) of a ball thrown upward \( t \) seconds after the ball was thrown is given by \( V(t)=20-9.8 t \). Calculate \( V(0) \) and \( V(1) \), and explain what these results mean.
Solution.
\( V(0)=20-9.8(0)=20 \) and \( V(1)=20-9.8(1)=10.2 \). These results indicate that the initial velocity of the ball is \( 20 \mathrm{~m} / \mathrm{s} \). After 1 second, the ball is traveling more slowly, at \( 10.2 \mathrm{~m} / \mathrm{s} \).
Do you want to try expressing real life situations as a function of an unknown variable? Answer Activity 6 below.

Given :

f(x)=2 x+1

g(x)=5 × 2

h(x)=x+3

1. (f ∘ g)(x)
2. (g=f)(x)
3. (h ∘ g)(x)
4. (f ∘ h)(x)

Finally, we are almost done with the preview of Functions!
Some real life situations can also be represented by functions. Take a closer look at how some events are written as functio is!

FUNCTIONS IN REAL-LIFE SITUATIONS
1) Suppose that s ( ( ) is the top speed (in km per hour) of a runner when the temperature is T degrees Celsius. Explain what the statements s(15)=12 and s(30) =10 mean.
Solution:
The first equation means that when the temperature is 15^∘C, then the top speed of a runner is 12 km per hour. However, when temperature rises to 30^∘C, the top speed is reduced to 10 km per hour.
2). The velocity V (in m / s ) of a ball thrown upward t seconds after the ball was thrown is given by V(t)=20-9.8 t. Calculate V(0) and V(1), and explain what these results mean.
Solution.
V(0)=20-9.8(0)=20 and V(1)=20-9.8(1)=10.2. These results indicate that the initial velocity of the ball is 20 m / s. After 1 second, the ball is traveling more slowly, at 10.2 m / s.
Do you want to try expressing real life situations as a function of an unknown variable? Answer Activity 6 below.

Added by Matthew H.

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