IB AA · 3A Concepts of a Function
Replace x with the given number, then simplify.
Substitute
Write the rule, replace every x with the input, then simplify.
Negatives
Put a negative input in parentheses before you multiply.
Solve f(x) = k
Set the rule equal to k and solve for x. That x is the input that produces k.
Fractions
Square a fraction before you multiply. Keep the exact fraction.
A linear rule and a positive input.
f(x) = 2x + 5
f(3) = 2(3) + 5
f(3) = 11
Answer: 11
f(x) = x + 6
f(4) = 4 + 6
f(4) = 10
Answer: 10
f(x) = 3x − 1
f(5) = 3(5) − 1
f(5) = 14
Answer: 14
f(x) = 2x + 9
f(0) = 2(0) + 9
f(0) = 9
Answer: 9
f(x) = 5x − 8
f(3) = 5(3) − 8
f(3) = 7
Answer: 7
f(x) = 4x + 2
f(6) = 4(6) + 2
f(6) = 26
Answer: 26
A negative input, or a quadratic.
f(x) = x² − 3x + 4
f(2) = (2)² − 3(2) + 4
f(2) = 4 − 6 + 4
f(2) = 2
Answer: 2
f(x) = −3x − 4
f(−2) = −3(−2) − 4
f(−2) = 2
Answer: 2
f(x) = x² − 4x + 1
f(5) = (5)² − 4(5) + 1
f(5) = 25 − 20 + 1
f(5) = 6
Answer: 6
f(x) = 2x² + x
f(−3) = 2(−3)² + (−3)
f(−3) = 18 − 3
f(−3) = 15
Answer: 15
f(x) = −x² + 6
f(2) = −(2)² + 6
f(2) = −4 + 6
f(2) = 2
Answer: 2
f(x) = x² + x − 6
f(−4) = (−4)² + (−4) − 6
f(−4) = 16 − 4 − 6
f(−4) = 6
Answer: 6
A fraction input, or an equation to solve.
q(x) = 3x² − 2
q(12) = 3(12)² − 2
q(12) = 34 − 2
q(12) = −54
Answer: −54
g(x) = 4x − 5
4x − 5 = 19
4x = 24
x = 6
Answer: x = 6
h(x) = x − 23
x − 23 = 7
x − 2 = 21
x = 23
Answer: x = 23
g(x) = 5x − 1
g(−3) = 5(−3) − 1
g(−3) = −16
5x − 1 = 14
5x = 15
x = 3
Answer: g(−3) = −16, x = 3
f(x) = x² − 2x
f(12) = (12)² − 2(12)
f(12) = 14 − 1
f(12) = −34
Answer: −34
f(x) = x² − 6x + 3
f(−1) = (−1)² − 6(−1) + 3
f(−1) = 1 + 6 + 3
f(−1) = 10
Answer: 10
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