Questions and Answers
Is the relation {(3,3),(5,5),(9,9)} a function?
What is the domain of the relation {(3,3),(5,5),(9,9)}?
{3,5,9}
What is the range of the relation {(3,3),(5,5),(9,9)}?
{3,5,9}
Is the relation {(2,5),(2,6),(5,5),(5,6)} a function?
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What is the domain of the relation {(2,5),(2,6),(5,5),(5,6)}?
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What is the range of the relation {(2,5),(2,6),(5,5),(5,6)}?
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How do you determine whether the equation x+y=46 defines y as a function of x?
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Does the equation x+y=4 define y as a function of x?
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Does the equation y=sqrt(x+31) define y as a function of x?
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Evaluate f(x)=9x−6 at x=2.
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Evaluate f(x)=9x−6 at x=x+5.
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Evaluate f(x)=9x−6 at x=-x.
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Evaluate h(x)=x^4 -4x^2 +7 at x=3.
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Evaluate h(x)=x^4 -4x^2 +7 at x=-1.
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Evaluate h(x)=x^4 -4x^2 +7 at x=-x.
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Evaluate h(x)=x^4 -4x^2 +7 at x=3a.
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Study Notes
Functions and Relations
- A relation is a function if each input (domain) corresponds to exactly one output (range).
- Example of a function: {(3,3), (5,5), (9,9)} has a domain of {3, 5, 9} and a range of {3, 5, 9}.
- Example of a non-function: {(2,5), (2,6), (5,5), (5,6)} because the input 2 produces two different outputs.
Identifying Functions from Equations
- To determine if an equation defines y as a function of x, rearrange it to solve for y.
- If a specific x value can produce multiple y values, the equation is not a function.
- The equation x + y = 4 is a function because it gives one unique y for each x.
- The equation y = √(x + 31) is a function since it’s explicitly solved for y, yielding one y for each x input.
Evaluating Functions
- To evaluate a function at specific values, substitute the values into the function expression and simplify.
- For f(x) = 9x - 6:
- f(2) = 12
- f(x + 5) = 9x + 39
- f(-x) = -9x - 6
- For h(x) = x⁴ - 4x² + 7:
- h(3) evaluates to 52
- h(-1) results in 4
- h(-x) remains as x⁴ - 4x² + 7, as it doesn’t change with -x input.
Studying That Suits You
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Description
Test your understanding of functions in Algebra Section 2.1 with these flashcards. Each card presents a relation, and you must determine if it is a function while identifying its domain and range. Perfect for reinforcing your algebra skills!
