H Algebra 2/Trig · Unit 1
Substitute an input into f or g, including linear and quadratic rules and negative inputs.
Function notation
f(a) means substitute a for every x in the rule, then simplify.
One function at a time
f and g are different rules. Use f’s rule for f(3) and g’s rule for g(3).
Negatives
When x is negative, keep the sign in parentheses: x² at x = −3 is (−3)² = 9.
Order
Square first, then multiply, then add. Follow the written rule, not a rewrite unless you mean to.
One linear rule. One input.
f(x) = 3x + 5
Substitute x = 4.
f(4) = 3(4) + 5
f(4) = 17
Answer: 17
g(x) = 2x − 7
Substitute x = 5.
g(5) = 2(5) − 7
g(5) = 3
Answer: 3
f(x) = −4x + 1
Substitute x = 3.
f(3) = −4(3) + 1
f(3) = −11
Answer: −11
h(x) = 5x − 2
Substitute x = −1.
h(−1) = 5(−1) − 2
h(−1) = −7
Answer: −7
f(x) = x + 8
Substitute x = −8.
f(−8) = (−8) + 8
f(−8) = 0
Answer: 0
g(x) = −2x − 3
Substitute x = −4.
g(−4) = −2(−4) − 3
g(−4) = 5
Answer: 5
A quadratic, or two linear evaluations.
f(x) = −x² + x + 4
Substitute x = 2.
f(2) = −(2)² + (2) + 4
f(2) = 2
Answer: 2
f(x) = −x² + 2x + 3
Substitute x = −2.
f(−2) = −(−2)² + 2(−2) + 3
f(−2) = −5
Answer: −5
f(x) = x² − 3x + 1
Substitute x = 4.
f(4) = (4)² − 3(4) + 1
f(4) = 5
Answer: 5
f(x) = 2x + 1
Substitute x = 5.
f(5) = 2(5) + 1
f(5) = 11
g(x) = 3x − 4
Substitute x = −2.
g(−2) = 3(−2) − 4
g(−2) = −10
Answer: a. 11b. −10
f(x) = −x + 6
Substitute x = 0.
f(0) = −(0) + 6
f(0) = 6
g(x) = 4x − 1
Substitute x = 3.
g(3) = 4(3) − 1
g(3) = 11
Answer: a. 6b. 11
f(x) = −x² + 9
Substitute x = 3.
f(3) = −(3)² + 9
f(3) = 0
Answer: 0
Two rules. Four evaluations, including a quadratic.
f(x) = −x² + 2x + 5
Substitute x = −2.
f(−2) = −(−2)² + 2(−2) + 5
f(−2) = −3
g(x) = 3x − 4
Substitute x = 5.
g(5) = 3(5) − 4
g(5) = 11
g(x) = 3x − 4
Substitute x = −1.
g(−1) = 3(−1) − 4
g(−1) = −7
f(x) = −x² + 2x + 5
Substitute x = 1.
f(1) = −(1)² + 2(1) + 5
f(1) = 6
Answer: a. f(−2) = −3b. g(5) = 11c. g(−1) = −7d. f(1) = 6
f(x) = −x² + x + 6
Substitute x = 3.
f(3) = −(3)² + (3) + 6
f(3) = 0
g(x) = 2x − 9
Substitute x = 4.
g(4) = 2(4) − 9
g(4) = −1
g(x) = 2x − 9
Substitute x = 0.
g(0) = 2(0) − 9
g(0) = −9
f(x) = −x² + x + 6
Substitute x = −1.
f(−1) = −(−1)² + (−1) + 6
f(−1) = 4
Answer: a. 0b. −1c. −9d. 4
f(x) = −x² + 3x + 2
Substitute x = 0.
f(0) = −(0)² + 3(0) + 2
f(0) = 2
g(x) = −2x + 5
Substitute x = −3.
g(−3) = −2(−3) + 5
g(−3) = 11
f(x) = −x² + 3x + 2
Substitute x = 2.
f(2) = −(2)² + 3(2) + 2
f(2) = 4
g(x) = −2x + 5
Substitute x = 1.
g(1) = −2(1) + 5
g(1) = 3
Answer: a. 2b. 11c. 4d. 3
f(x) = x² − 4x
Substitute x = 4.
f(4) = (4)² − 4(4)
f(4) = 0
g(x) = 5x + 1
Substitute x = −1.
g(−1) = 5(−1) + 1
g(−1) = −4
f(x) = x² − 4x
Substitute x = −2.
f(−2) = (−2)² − 4(−2)
f(−2) = 12
g(x) = 5x + 1
Substitute x = 2.
g(2) = 5(2) + 1
g(2) = 11
Answer: a. 0b. −4c. 12d. 11
f(x) = −x² + 2x − 3
Substitute x = −4.
f(−4) = −(−4)² + 2(−4) − 3
f(−4) = −27
Answer: −27
g(x) = −5x + 2
Substitute x = −6.
g(−6) = −5(−6) + 2
g(−6) = 32
Answer: 32
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