Question

name:
pa evaluate and interpret graphs
date: pd

1. mal built a model racer to race for a school competition. ( m(t) ) gives mals cars distance after ( t ) seconds. use the graph to determine the missing value in each function statement.

Explanation:

Step1: Find \(m(\_\_)=10\)

Looking at the graph, when the distance \(m(t) = 10\), the time \(t = 6\) (from the point \((6,10)\)).

Step2: Find \(m(10)\)

Looking at the graph, when \(t = 10\), the distance \(m(10)=12\) (from the point \((10,12)\)).

Step3: Find \(m(15)\)

Looking at the graph, when \(t = 15\), the distance \(m(15)=12\) (from the point \((15,12)\)).

Step4: Find \(m(22)\)

Looking at the graph, when \(t = 22\), the distance \(m(22)=22\) (from the point \((22,22)\)).

Step5: Find \(m(\_\_)=46\)

Assuming the last - point on the graph (since the graph seems to end at a distance of \(46\)), if we assume the last - time value (from the x - axis scale), when \(m(t)=46\), \(t = 26\) (by observing the x - axis and the end - point of the graph).

Answer:

\(m(6) = 10\); \(m(10)=12\); \(m(15)=12\); \(m(22)=22\); \(m(26)=46\)

For the meaning:

• \(m(6) = 10\) means that after \(6\) seconds, Mai's car has traveled a distance of \(10\) units (the units of distance are not specified in the problem, but from the y - axis label "Distance [units]").
• \(m(10)=12\) means that after \(10\) seconds, Mai's car has traveled a distance of \(12\) units.
• \(m(15)=12\) means that from \(t = 10\) to \(t = 15\) seconds, the car has not moved forward (it is at rest or moving at a very slow speed that does not change the distance measurement in the context of this graph).
• \(m(22)=22\) means that after \(22\) seconds, Mai's car has traveled a distance of \(22\) units.
• \(m(26)=46\) means that after \(26\) seconds, Mai's car has traveled a distance of \(46\) units.