Key takeaway: Function notation writes a function as a name followed by its input in parentheses, such as f(x), so f(4) means the output when the input is 4.
Grade 9 – Algebra 1F-IF.A.2Functions and Graphs
Definition of Function Notation
Function notation gives a rule a short name and shows which number is going in. In \(f(x) = 3x – 7\), the letter \(f\) names the function and \(x\) is the input. The expression \(f(x)\) is read “f of x” and stands for the output.
To evaluate, replace every \(x\) with the given input, then simplify with the order of operations. Any letter can name a function: \(C(h)\) can mean cost after \(h\) hours and \(T(d)\) the temperature on day \(d\). Using different letters is helpful when several functions appear in the same problem.
Formula and notation
The input sits inside the parentheses, and the output is what the whole expression equals:
\[f(4) = 3(4) – 7 = 5\]
In function notation this says the input 4 gives the output 5, which corresponds to the point \((4, 5)\) on the graph. The parentheses are not multiplication.
Key facts
- f(x) is the output y for the input x, so y and f(x) are interchangeable.
- f(a) = b means the graph contains the point (a, b).
- Function notation uses a different name, such as g or C, for a different function.
- The input can be a number, a variable or a whole expression like x + 2.
Function Notation example
A kayak shop charges a \$18 launch fee plus \$9.50 per hour. The cost function is \(C(h) = 18 + 9.5h\). Find \(C(4)\) and tell what it means.
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Replace \(h\) with 4: \(C(4) = 18 + 9.5(4)\).
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Multiply first: \(9.5 \times 4 = 38\).
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Add: \(18 + 38 = 56\).
\(C(4) = \) \$56: renting a kayak for 4 hours costs \$56.
Common mistake
Watch out
Asked for \(C(4)\), Wren reads it as “C times 4” and tries to multiply 4 by the cost.
Why it is wrong
In \(C(4)\) the parentheses hold the input; they do not mean multiplication. \(C(4)\) is the cost when \(h = 4\) hours. Substitute 4 for \(h\) in the rule to get \$56.
Related terms and lessons
- Function
- Domain and Range
- Independent Variable
- Dependent Variable
- Linear Function
- Vertical Line Test
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