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Algebra 1

4.12.4 Using Graphs to Determine the Domain of a Function

Algebra 14.12.4 Using Graphs to Determine the Domain of a Function

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Activity

Consider the function f(x)=6x2f(x)=6x2.

To find out the sets of possible input and output values of the function, Clare created a table and evaluated ff at some values of xx. Along the way, she ran into some trouble.

1. Find f(x)f(x) for each xx-value Clare listed. Describe what Clare’s trouble might be.

xx -10 0 1212 2 8
f(x)f(x)          

2. Use graphing technology to graph function ff. What do you notice about the graph?

3. Use a calculator to compute the value you and Clare had trouble computing. What do you notice about the computation?

4. How would you describe the domain of function ff?

Are you ready for more?

Extending Your Thinking

Why do you think the graph of function ff looks the way it does? Why are there two parts that split at x=2x=2, with one curving down as it approaches x=2x=2 from the left and the other curving up as it approaches x=2x=2 from the right?

Evaluate function ff at different xx-values that approach 2 but are not exactly 2, such as 1.8, 1.9, 1.95, 1.999, 2.2, 2.1, 2.05, 2.001, and so on. What do you notice about the values of f(x)f(x) as the xx-values get closer and closer to 2?

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