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Questions and Answers
Which of the following best describes the domain of a function?
Which of the following best describes the domain of a function?
- The set of all possible inputs for the function
- The set of all values that the function takes
- The set of all values for which the function is defined (correct)
- The set of all possible outputs for the function
What is the range of a function?
What is the range of a function?
- The set of all possible inputs for the function
- The set of all values for which the function is defined
- The set of all possible outputs for the function
- The set of all values that the function takes (correct)
What is another term for the domain of a function?
What is another term for the domain of a function?
- Output set
- Solution set
- Input set
- Replacement set (correct)
What is another term for the range of a function?
What is another term for the range of a function?
When is a value not in the range of a function?
When is a value not in the range of a function?
Which step is necessary when solving absolute value equations?
Which step is necessary when solving absolute value equations?
What must the sign of [latex]\left| x \right|[/latex] be when solving absolute value equations?
What must the sign of [latex]\left| x \right|[/latex] be when solving absolute value equations?
What can the expression [latex]x[/latex] be when solving absolute value equations?
What can the expression [latex]x[/latex] be when solving absolute value equations?
What must the value of [latex]a[/latex] be on the right side of the equation when solving absolute value equations?
What must the value of [latex]a[/latex] be on the right side of the equation when solving absolute value equations?
What is the general approach for breaking down an absolute value equation into two equations?
What is the general approach for breaking down an absolute value equation into two equations?
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Study Notes
The Domain of a Function
- The domain of a function is the set of all possible input values (x-values) for which the function is defined.
The Range of a Function
- The range of a function is the set of all possible output values (y-values) that the function can produce.
Other Terms for Domain
- Input
Other Terms for Range
- Output
When a Value is Not in the Range
- A value is not in the range of a function if there is no input value that produces that output value.
Solving Absolute Value Equations
- When solving absolute value equations, it is necessary to isolate the absolute value expression.
Sign of [latex]\left| x \right|[/latex]
- The sign of [latex]\left| x \right|[/latex] must be positive or zero when solving absolute value equations.
The Expression [latex]x[/latex]
- The expression [latex]x[/latex] can be positive, negative, or zero when solving absolute value equations.
Value of [latex]a[/latex]
- The value of [latex]a[/latex] on the right side of the equation must be non-negative when solving absolute value equations.
Breaking Down Absolute Value Equations
- To break down an absolute value equation into two equations, separate the equation into two cases: one where the expression inside the absolute value is positive, and another where it is negative.
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