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FUNCTION REVISION QUESTIONS

Functions in Mathematics – 30 Questions

A. Basic Concepts (1–10)

  1. Define a function in your own words.
  2. Is the relation \(\{(1, 2), (2, 3), (3, 4)\}\) a function? Why?
  3. Which of the following is not a function?
    A) \(f(x) = x^2\)
    B) \(f(x) = \sqrt{x}\)
    C) \(f(x) = \frac{1}{x}\)
    D) \(f(x) = \pm\sqrt{x}\)
  4. Find the domain of the function \(f(x) = \frac{2}{x - 5}\).
  5. Does the graph of a vertical line represent a function? Explain.
  6. What is the range of \(f(x) = x^2\) for real values of \(x\)?
  7. State the domain and range of \(f(x) = \sqrt{x + 3}\).
  8. If \(f(x) = 2x + 1\), find \(f(4)\).
  9. Does the equation \(x = y^2\) represent a function? Explain why or why not.
  10. Explain why every linear equation of the form \(y = mx + c\) (where \(m \neq 0\)) is a function.

B. Function Notation and Evaluation (11–20)

  1. If \(f(x) = 3x - 4\), find \(f(-2)\).
  2. Given \(f(x) = x^2 - 2x\), find \(f(a + 1)\).
  3. If \(f(x) = \frac{1}{x + 2}\), evaluate \(f(-1)\).
  4. Given \(f(x) = x^2\) and \(g(x) = x + 2\), find \(f(g(2))\).
  5. If \(f(x) = 2x + 3\), solve for \(x\) when \(f(x) = 11\).
  6. Let \(f(x) = x^2 - 5x + 6\). Find the zeros of \(f(x)\).
  7. Evaluate \(f(2x)\) if \(f(x) = x^2 + 1\).
  8. Find the inverse of the function \(f(x) = 2x + 3\).
  9. Verify whether the function \(f(x) = \frac{x - 2}{x + 2}\) is one-to-one.
  10. Given \(f(x) = x^2\), find the value(s) of \(x\) for which \(f(x) = 25\).

C. Advanced and Word Problems (21–30)

  1. If \(f(x) = 3x + 1\) and \(g(x) = 2x - 5\), find \((f + g)(x)\).
  2. Given \(f(x) = \sqrt{x + 4}\), state the domain of \(f\).
  3. The output of a function triples the input and subtracts 2. Write the function rule.
  4. If \(f(x) = x^2 + x\) and \(g(x) = x - 1\), find \((f \circ g)(x)\).
  5. A function maps the number of hours worked, \(h\), to the amount earned: \(E(h) = 10h\). How much is earned for 6.5 hours?
  6. Let \(f(x) = |x - 2|\). Describe the shape of its graph.
  7. Determine whether \(f(x) = x^3\) is increasing or decreasing.
  8. If \(f(x) = 2x\), find the expression for the inverse function \(f^{-1}(x)\).
  9. A temperature in Fahrenheit is given by \(F(C) = \frac{9}{5}C + 32\). Find \(F(20)\).
  10. Describe a function whose domain is all real numbers except \(x = 1\) and \(x = -1\).

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