Let’s solve each problem one by one. We’ll plug in the given value into the function and simplify carefully.
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1) q(m) = 10m, Find q(2)
Plug in m = 2:
q(2) = 10 × 2 =
20
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2) b(w) = -2w² - 11, Find b(-10)
Plug in w = -10:
First, square -10 → (-10)² = 100
Then multiply by -2 → -2 × 100 = -200
Then subtract 11 → -200 - 11 =
-211
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3) x(g) = 2g² + 7g, Find x(11)
Plug in g = 11:
g² = 121 → 2×121 = 242
7g = 7×11 = 77
Add them: 242 + 77 =
319
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4) y(w) = w³ + 8w², Find y(9)
Plug in w = 9:
w³ = 9×9×9 = 729
w² = 81 → 8×81 = 648
Add: 729 + 648 =
1377
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5) z(n) = 3^(n+2), Find z(1)
Plug in n = 1:
Exponent becomes 1 + 2 = 3
So z(1) = 3³ = 3×3×3 =
27
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6) b(n) = (-3)^(2n), Find b(1)
Plug in n = 1:
Exponent = 2×1 = 2
So b(1) = (-3)² = (-3)×(-3) =
9
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7) b(s) = -10s, Find b(s - 11)
This means replace every “s” with “(s - 11)”
b(s - 11) = -10 × (s - 11) =
-10s + 110
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8) k(z) = z² + 7, Find k(8z - 2)
Replace z with (8z - 2):
k(8z - 2) = (8z - 2)² + 7
First expand (8z - 2)²:
= (8z)² - 2×8z×2 + (-2)² = 64z² - 32z + 4
Now add 7: 64z² - 32z + 4 + 7 =
64z² - 32z + 11
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9) z(q) = -10q² - 5q, Find z(q²)
Replace every q with q²:
z(q²) = -10(q²)² - 5(q²) = -10q⁴ - 5q²
Answer:
-10q⁴ - 5q²
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10) y(z) = z³ - 11z², Find y(10z)
Replace z with 10z:
y(10z) = (10z)³ - 11(10z)²
Calculate:
(10z)³ = 1000z³
(10z)² = 100z² → 11×100z² = 1100z²
So: 1000z³ - 1100z²
Answer:
1000z³ - 1100z²
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11) p(d) = 3^(2d+2), Find p(d + 11)
Replace d with (d + 11):
p(d + 11) = 3^[2(d + 11) + 2]
Simplify exponent:
2(d + 11) = 2d + 22 → +2 more → 2d + 24
So:
3^(2d + 24)
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12) q(p) = -3^(2p), Find q(9p)
Note: This is written as -3^(2p), which usually means -(3^(2p)), not (-3)^(2p).
But let’s check context — in #6 it was written as (-3)^(2n), so here since no parentheses, we assume it’s negative of 3 to the power.
So q(p) = - (3^(2p))
Now find q(9p): replace p with 9p
→ q(9p) = - (3^(2×9p)) = - (3^(18p))
Answer:
-3^(18p)
*(If the original meant (-3)^(2p), then answer would be different — but based on standard order of operations and how it's written without parentheses around -3, we go with -[3^(2p)])*
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Final Answer:
1) 20
2) -211
3) 319
4) 1377
5) 27
6) 9
7) -10s + 110
8) 64z² - 32z + 11
9) -10q⁴ - 5q²
10) 1000z³ - 1100z²
11) 3^(2d + 24)
12) -3^(18p)
Parent Tip: Review the logic above to help your child master the concept of function operations algebra 2 worksheet.
