This algebra 1 building test answer key gives the full solution and the scoring guide for each of the 9 test questions on building functions and inverses.
Each solution is followed by a scoring guide. Award points for correct setup even if a later arithmetic slip occurs, but give no point for a final answer that has no supporting work. The total is 20 points.
Algebra 1 Building Test Answer Key: questions 1–5
Question 1: Build from a situation (2 points)
- \(f(h)=6h+10\).
- \(f(0)=10\) and \(f(h)=f(h-1)+6\).
Scoring: 1 point for the explicit rule with the correct rate and fee; 1 point for a correct start value and a repeated change of 6.
Question 2: Steps of a function (2 points)
- \(g(x)=5(x-4)\), with parentheses because the subtraction happens first.
- \(g(9)=5(9-4)=25\).
Scoring: 1 point for the expression with the subtraction grouped; 1 point for the value 25.
Question 3: Combine functions (2 points)
- \((f+g)(x)=4x+1+x-6=5x-5\).
- \((f-g)(x)=4x+1-(x-6)=3x+7\) and \((f-g)(3)=16\).
Scoring: 1 point for the sum; 1 point for the difference with the sign distributed and the correct value 16. Check: \(f(3)=13\), \(g(3)=-3\), \(13-(-3)=16\).
Question 4: T-shirt profit (3 points)
- \(P(x)=12x-(5x+140)=7x-140\).
- \(7x-140=0\) gives \(x=20\) shirts.
- \(P(35)=7(35)-140=105\), a profit of $105.
Scoring: 1 point per part; in (a) the whole cost must be subtracted.
Question 5: Solve f(x) = c (2 points)
- \(-3x+14=5\), so \(-3x=-9\) and \(x=3\).
- \(-3x+14=-7\), so \(-3x=-21\) and \(x=7\).
Scoring: 1 point each for the correct value of x. Check: \(f(3)=5\), \(f(7)=-7\).
Algebra 1 Building Test Answer Key: questions 6–9
Question 6: Inverse of a linear function (3 points)
- \(y=\frac{2}{3}x+4\), so \(y-4=\frac{2}{3}x\) and \(x=\frac{3}{2}(y-4)=\frac{3}{2}y-6\).
- \(x=\frac{3}{2}(10-4)=9\). Check: \(f(9)=6+4=10\).
Scoring: 1 point for isolating the term with x; 1 point for multiplying by the reciprocal correctly; 1 point for the value 9.
Question 7: Water tank (3 points)
- \(150-6t=90\), so \(6t=60\) and \(t=10\) minutes.
- \(6t=150-W\), so \(t=\frac{150-W}{6}\).
- \(t=\frac{150-0}{6}=25\) minutes.
Scoring: 1 point per part.
Question 8: Constant rate in a table (2 points)
- Mei is correct: \(x\) rises by 2 and \(y\) rises by 6 in every step (\(14-8=6\), \(20-14=6\), \(26-20=6\)).
- \(\frac{6}{2}=3\) per 1 unit of \(x\).
Scoring: 1 point for comparing equal x-steps with equal y-changes; 1 point for the rate 3.
Question 9: Check an inverse (1 point)
\(f(5)=13\) and \(g(13)=\frac{10}{2}=5\), the original input, which is consistent with \(g\) being the inverse of \(f\).
Scoring: 1 point for the value 5 with a correct conclusion.
Scoring summary
20 points: add the points of every question of this algebra 1 building test answer key.
How to use this algebra 1 building test answer key
Use this algebra 1 building test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Algebra 1 Building Functions and Inverses test answer key
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