Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
1. Parent Functions and Transformations
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Exercise 41 Page 9

What you can say about the function by using its rule?

Function Family: Linear.
Domain: All real numbers.
Range: All real numbers.

Practice makes perfect

We want to find out a few pieces of information about the given function.

  1. What family does the function belong to?
  2. What is the domain of this function?
  3. What range does the function have?

Let's answer these questions!

Function Family

Look carefully at the function rule.

g(x)=3x+4 We can see that given function is linear. Therefore, it belongs to the family of linear functions, with a parent function of y=x.

Domain

Unless specific restrictions are given, the domain of linear functions is usually all real numbers. Domain:& - ∞ < x < ∞

Range

Unless specific restrictions are given, the range of linear functions is also all real numbers. Range:& - ∞ < x < ∞

Checking the Answer

To verify your answer, enter the function rule in the calculator by pushing Y= and writing the function rule in the first row. Next, by pushing GRAPH, the calculator will draw the graph of the function.

TI räknarfönster för window
Window with a graph

Looking at the graph, we can confirm that our solution is correct.