Introduction to Functions: math test solutions, Grade 8 – download the PDF

1 Function or not? / 4 pts

1. Yes: each input appears once; the repeated output 3 is allowed. (1 pt)
2. No: the input 4 has outputs 1 and 2. (1 pt)
3. No: a vertical line at \(x = 2\) meets the graph twice. (1 pt)
4. Yes: every input has exactly one square. (1 pt)

2 Reading a table / 4 pts

1. \(\dfrac{11 - 5}{2 - 0} = 3\). (1.5 pts)
2. The output at \(x = 0\) is 5. (0.5 pt)
3. \(y = 3x + 5\). (1 pt)
4. \(3(10) + 5 = 35\). (1 pt)

3 Linear or nonlinear? / 3 pts

1. Linear: of the form \(y = mx + b\). (1 pt)
2. Nonlinear: \(x\) is cubed, the graph is a curve. (1 pt)
3. Nonlinear: the changes are \(2, 4, 8\), not constant. (1 pt)

4 A swimming pool / 4 pts

1. \(V = 600 - 25t\). (1 pt)
2. 600 is the initial volume in gallons; \(-25\) is the rate of change: the volume drops 25 gallons per minute. (1 pt)
3. \(600 - 250 = 350\) gallons. (1 pt)
4. \(600 - 25t = 0 \Rightarrow t = 24\) minutes. (1 pt)

5 Comparing two functions / 3 pts

1. For \(f\), the rate is 4. For \(g\): \(\dfrac{15 - 9}{3 - 0} = 2\). (1 pt)
2. \(f\) starts at 3 and \(g\) starts at 9: \(g\) has the greater initial value. (1 pt)
3. \(g(x) = 2x + 9\). \(4x + 3 = 2x + 9 \Rightarrow 2x = 6 \Rightarrow x = 3\); both outputs are 15. (1 pt)

6 Sketch from a story / 2 pts

Key points after the start: \((10, 60)\), \((15, 60)\) and \((25, 0)\). (1 pt) The graph rises, stays flat, then falls. (1 pt)