Function Notation and Evaluation
Practice reading f(x), evaluating from equations, tables, and graphs, and handling composition.
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Questions Covered in This Set
12 cards to master
How do you read f(x) = 3x + 2 aloud, and what does f mean?
"f of x equals 3x plus 2." The letter f is the NAME of the rule; x is the input slot. f(x) does NOT mean f times x.
If f(x) = 3x + 2, what is f(-5)?
f(-5) = 3(-5) + 2 = -15 + 2 = -13
If f(x) = x² - 4x, what is f(-3)?
f(-3) = (-3)² - 4(-3) = 9 + 12 = 21. Always put parentheses around a negative input.
If f(x) = x² - 4x, find f(x + 1) in simplified form.
(x+1)² - 4(x+1) = x² + 2x + 1 - 4x - 4 = x² - 2x - 3
What's the difference between finding f(3) and solving f(x) = 3?
f(3) means substitute the INPUT 3. Solving f(x) = 3 means set the rule equal to the OUTPUT 3 and solve for x.
If f(x) = 3x + 2 and f(x) = 17, what is x?
3x + 2 = 17 → 3x = 15 → x = 5, so f(5) = 17.
On a graph, what does f(a) = b tell you?
The point (a, b) lies on the graph. Horizontal position = input, vertical height = output.
How do you solve f(x) = 5 using a graph?
Draw the horizontal line y = 5 and read the x-coordinates of every point where it intersects the graph.
If f(x) = 2x and h(x) = x + 6, find f(h(1)).
Work inside out: h(1) = 7, then f(7) = 14. (Note h(f(1)) = h(2) = 8 — order matters.)
If C(t) = 45 + 12t is cost in dollars after t months, what does C(9) = 153 mean?
After 9 months the total cost is $153. The 45 is the one-time fee (value at t = 0) and 12 is the monthly rate.
From the table x: 1,2,3,4 with g(x): 7,4,4,-1 — for what x is g(x) = 4?
x = 2 and x = 3. One input gives one output, but different inputs can share the same output.
If f(x) = x² - 2x + 1 and g(x) = 4 - x, simplify f(x) - g(x).
x² - 2x + 1 - (4 - x) = x² - x - 3 (distribute the minus sign!)
