The function $f$ represents the distance of a dog from a post in feet as a function of time $t$ in seconds. We need to write three true statements about this situation using function notation. At least one statement should use the "$=$" sign and another statement should use the "$<$" sign.

1. Problem Description

The function $f$ represents the distance of a dog from a post in feet as a function of time $t$ in seconds. We need to write three true statements about this situation using function notation. At least one statement should use the "$=$" sign and another statement should use the "$<$" sign.

2. Solution Steps

Let's analyze the graph. We can identify some points on the graph.

- At $t=0$, $f(0) = 1.5$.

- At $t=60$, $f(60) = 4$.

- At $t=100$, $f(100) \approx 2.2$.

Statement 1 (using the = sign):

From the graph, we can see that when $t = 60$ seconds, the distance of the dog from the post is 4 feet. So, $f(60) = 4$.

Statement 2 (using the < sign):

From the graph, we can see that the distance at $t=0$ is about 1.5 feet, and the distance at $t=100$ is about 2.2 feet. Therefore, $f(0) < f(100)$. In other words, the distance at time 0 is less than the distance at time

1

0

0.

Statement 3:

We can also say that the distance at $t=20$ is approximately 3.4 feet.

The distance at $t=40$ is approximately 5.1 feet. Therefore, $f(20) < f(40)$.

3. Final Answer

Here are the three statements:

1. $f(60) = 4$

2. $f(0) < f(100)$

3. $f(20) < f(40)$