Functions, Domain, Range and Function Notation: Algebra 1 Math Test Answer Key – PDF Download

Question 1: Is it a function? (3 points)

1. The inputs \(-1, 0, 1, 2\) are all different. Yes. (The repeated output 2 is allowed.)
2. The input 6 appears twice, with outputs 3 and 8. No.
3. The line \(x=0\) meets the circle at \((0,3)\) and \((0,-3)\). No.

Scoring: 1 point per part for the correct answer with a valid reason. An answer of Yes or No with no reason earns half credit.

Question 2: Evaluate a quadratic (2 points)

1. \(f(-2)=4+8+1=13\). 13
2. \(f(5)=25-20+1=6\). 6

Scoring: 1 point per correct value. Give half credit if the substitution is right but there is an arithmetic slip.

Question 3: Evaluate and solve (2 points)

1. \(g(-4)=-3(-4)+8=12+8=20\). 20
2. \(-3x+8=-7\), \(-3x=-15\), \(x=5\). \(x=5\)

Scoring: 1 point per part. In part (b), award the point for the correct value of \(x\).

Question 4: Read values from a graph (3 points)

1. \(f(0)=3\)
2. \(f(1)=4\)
3. \(x=-1\) and \(x=3\)

Scoring: 1 point per part. In part (c), both values are needed for the point.

Question 5: Ticket profit (2 points)

1. \(P(40)=240-150=90\). Selling 40 tickets gives a profit of \(\$90\).
2. \(6n-150=0\) gives \(6n=150\), so \(n=25\). Selling 25 tickets gives no profit and no loss (break-even).

Scoring: 1 point per part: 0.5 for the value and 0.5 for a correct interpretation with units.

Question 6: Domain and range of a graph (3 points)

1. \(-3\le x < 2\)
2. \(-1\le y < 4\)
3. Continuous: the graph is connected, so every value between the endpoints is allowed.

Scoring: 1 point per part. In parts (a) and (b), the point requires the correct open and closed ends.

Question 7: Notebook sale (2 points)

1. Only whole numbers make sense. \(\{1,2,3,4,5,6,7,8\}\)
2. Multiply each by 2.5. \(\{2.50,\ 5.00,\ 7.50,\ 10.00,\ 12.50,\ 15.00,\ 17.50,\ 20.00\}\) dollars

Scoring: 1 point per part. An answer that lists all numbers from 2.50 to 20.00 earns 0 for part (b).

Question 8: Rocket launch (3 points)

1. \(h(3)=-144+192=48\). 48 ft
2. \(h(4)=-256+256=0\). 4 seconds after launch, the rocket is back on the ground.
3. The flight lasts from \(t=0\) to \(t=4\). The highest point is \(h(2)=-64+128=64\). Domain \(0\le t\le 4\); range \(0\le h\le 64\).

Scoring: 1 point per part. In part (c), both the domain and the range must be correct for the point.

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