Skip to content
Home › Test solutions › Grade 9 › Relations and Functions: math test solutions, Grade 9

Relations and Functions: math test solutions, Grade 9 – download the PDF

  • by
Rate this post
Test solutions Grade 9 : Relations and Functions — Zyro the alien explorer of Planète Maths

Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

1 Relations / 4 pts

  1. Domain \(\{0, 1, 2, 5\}\); range \(\{-3, 4, 6\}\). (1 pt)
  2. Yes: every input appears once. (1 pt)
  3. The inputs \(0\) and \(2\). (1 pt)
  4. For example replace \((5, -3)\) by \((0, -3)\): the input \(0\) then has the outputs \(6\) and \(-3\). (1 pt)

2 Function notation / 4 pts

  1. \(f(3) = -6 + 9 = 3\). (1 pt)
  2. \(f(-4) = 8 + 9 = 17\). (1 pt)
  3. \(-2x + 9 = 1\), \(-2x = -8\), \(x = 4\). (1 pt)
  4. \(-2x + 9 = -5\), \(-2x = -14\), \(x = 7\). (1 pt)

3 Reading a graph / 4 pts

  1. \(h(2) = -4 + 8 = 4\), the top of the curve. (1 pt)
  2. \(h(x) = 0\) at \(x = 0\) and \(x = 4\). (1 pt)
  3. \(h(1) = 3\) and \(h(3) = -9 + 12 = 3\), so \(x = 1\) and \(x = 3\). (1 pt)
  4. The highest value is \(4\). The ends give \(h(-1) = -5\) and \(h(5) = -5\), the lowest values. The range is \(-5 \le y \le 4\). (1 pt)

4 Table and rule / 3 pts

  1. Domain \(\{0, 2, 4, 6\}\); range \(\{1, 7, 13, 19\}\). (1 pt)
  2. When \(x\) goes up by \(2\), \(f(x)\) goes up by \(6\): the slope is \(3\), and \(f(0) = 1\). So \(f(x) = 3x + 1\). (1 pt)
  3. \(f(15) = 45 + 1 = 46\). (1 pt)

5 Arithmetic sequence / 3 pts

  1. \(d = 8 - 11 = -3\), and \(a_n = 11 - 3(n - 1) = 14 - 3n\). (1 pt)
  2. \(a_9 = 14 - 27 = -13\). (1 pt)
  3. \(14 - 3n < 0\) gives \(n > 4.67\), so \(n = 5\) and \(a_5 = -1\) (while \(a_4 = 2\)). (1 pt)

6 Gym membership / 2 pts

  1. \(C(m) = 12m + 25\); \(C(8) = 96 + 25 = 121\) dollars. (1 pt)
  2. \(12m + 25 \le 200\) gives \(m \le 14.58\), so 14 months. Check: \(C(14) = 193\) and \(C(15) = 205\). (1 pt)
Back to the test : Relations and Functions: math test solutions, Grade 9 – Planète MathsReview the lesson : Relations and Functions: math test solutions, Grade 9 – Planète Maths

Test yourself: quick challenge for Grade 9

🚀 Keep exploring with Zyro

Relations and Functions: math test, Grade 9📝 Math testsRelations and Functions: math test, Grade 9Relations and Functions: math lesson, Grade 9📘 Math lessonsRelations and Functions: math lesson, Grade 9Relations and Functions: math quiz, Grade 9🎯 Math quizzesRelations and Functions: math quiz, Grade 9Slope and Graphing Linear Functions: math test, Grade 9📝 Math testsSlope and Graphing Linear Functions: math test, Grade 9Writing Linear Equations and Scatter Plots: math test, Grade 9📝 Math testsWriting Linear Equations and Scatter Plots: math test, Grade 9Slope and Graphing Linear Functions: math lesson, Grade 9📘 Math lessonsSlope and Graphing Linear Functions: math lesson, Grade 9