Question

1. write three statements that are true about this situation. use function notation.

function f gives the distance of a
dog from a post, in feet, as a function
of time, t, in seconds, since its owner
left.
use the = sign in at least one
statement and the < sign in another
statement.
chart: distance from post in feet (y-axis) vs time in seconds (x-axis), with a curve and a dot at (60,4)

Explanation:

Step1: Analyze the initial time

At \( t = 0 \) (when the owner just left), the distance from the post is the y - intercept. From the graph, when \( t = 0 \), \( f(0)=1.5 \) (approximate value from the graph's y - axis at \( t = 0 \)).

Step2: Analyze the point at t = 60

We can see from the graph that at \( t = 60 \) seconds, the distance from the post is 4 feet. So we can write \( f(60)=4 \).

Step3: Analyze a comparison

We can compare two function values. For example, at \( t = 0 \), \( f(0)=1.5 \) and at \( t = 100 \), let's assume from the graph that \( f(100)\approx2.5 \). So we can write \( f(0)<f(100) \). Also, we can make another statement, for example, as time increases from \( t = 60 \) to \( t = 100 \), the distance from the post decreases, so \( f(60)>f(100) \) (using the values we estimated, \( 4>2.5 \)).

Answer:

1. \( f(0)=1.5 \) (The dog is 1.5 feet from the post when the owner just left, \( t = 0 \) seconds).
2. \( f(60)=4 \) (The dog is 4 feet from the post at \( t = 60 \) seconds).
3. \( f(0)<f(100) \) (The distance of the dog from the post at \( t = 0 \) seconds is less than the distance at \( t = 100 \) seconds).