Connecting Representations of Functions
Let’s connect tables, equations, graphs, and stories of functions.
The equation and the tables represent two different functions. Use the equation \(b=4a-5\) and the table to answer the questions. This table represents \(c\) as a function of \(a\).
- When \(a\) is -3, is \(b\) or \(c\) greater?
- When \(c\) is 21, what is the value of \(a\)? What is the value of \(b\) that goes with this value of \(a\)?
- When \(a\) is 6, is \(b\) or \(c\) greater?
- For what values of \(a\) do we know that \(c\) is greater than \(b\)?
Elena and Lin are training for a race. Elena runs her mile at a constant speed of 7.5 miles per hour.
Lin’s total distances are recorded every minute:
Who finished their mile first?
This is a graph of Lin’s progress. Draw a graph to represent Elena’s mile on the same axes.
For these models, is distance a function of time? Is time a function of distance? Explain how you know.
Match each function rule with the value that could not be a possible input for that function.
Find a value of \(x\) that makes the equation true. Explain your reasoning, and check that your answer is correct.
\(\displaystyle \text-(\text-2x+1)= 9-14x\)