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Federal (FBISE) · Chapter test · Free

10th Class Mathematics Chapter 6 Test06. Functions and Graphs

26 marks · 40 minutes · 17 questions. Covers: 06. Functions and Graphs.

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10th Class Mathematics Chapter 6 Test

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 26Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 6 × 1 = 6)

  1. If f(x)=12xf(x) =\frac{1}{2} x , what is f2(x)f^2 (x) ?
    1. 14x \frac{1}{4x}
    2. 14x \frac{1}{4} x
    3. 2x
    4. 14x2 \frac{1}{4} x^2
  2. Which of the following is an exponential function?
    1. (13)x\left(\frac{1}{3}\right)^x
    2. exe^x
    3. 2x2^x
    4. All of these
  3. What is the domain of the relation g = {(1, 0), (2, 2), (3, 0), (2, 4)}?
    1. {0, 1, 2, 3}
    2. {0, 2, 4}
    3. {1, 2, 3}
    4. {0, 1, 2, 3, 4}
  4. At what point will the graph of y=2x2−1y = 2x^2 - 1 cuts y-axis?
    1. (±12,0)\left( \pm \frac{1}{\sqrt{2}}, 0 \right)
    2. -1
    3. (0, -1)
    4. (-1, 0)
  5. If y = 2x - 1, what is f−1(x)f^{-1}(x)?
    1. 1+y2\frac{1 + y}{2}
    2. 2y - 1
    3. 1+x2\frac{1 + x}{2}
    4. y + 1
  6. f A = {−2, 0, 2}and B = {0, 2} and f : A → B is defined as f = {(−2, 2), (0, 0), (2, 0)}, what type of function is f?
    1. into
    2. onto
    3. injective
    4. bijective

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Sketch the graph of the quadratic function y = −x²− 4x. Will it open upward or downward?
  2. If f:R→R f : \mathbb{R} \to \mathbb{R} is defined by f(x)=3x+12 f(x) = 3x + \frac{1}{2} , find f−1(x) f^{-1}(x) .
  3. Find the inverse of the following function. g(x) = (x − 3)², x ≥ 3
  4. The profit (in rupees) of a company is given by the function P(x) = |2x - 100|, where x is the number of units sold. If 120 units are sold, what is the profit?
  5. If f(x)=x2−12x+3, f(x) = x^2 - \frac{1}{2}x + 3, , evaluate the following. f(-1)
  6. Identify the graph of linear and non-linear function from the following? Also indicate the graphs which are graphs of functions by applying vertical line test.Question diagram
  7. Find the value of f(x) = -2x³ + x² at: f(x + 2)
  8. Check whether the curve (parabola) drawn for the following functions will open upwards or downwards. Also find x-intercept, y-intercept and sketch the graph of the given function. f(x) = −x²+ 2x + 3

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Find inverse off(x)=3x2x−1 f(x) = \frac{3x}{2x-1} . At what value of the variable, f−1(x)f^{-1}(x)will be undefined? Also f−1(=1)f^{-1}(=1).
  2. A researcher studies the spread of a disease and finds that the number of infected people grows according to the function f(t) = 10(1.2)t , where t is time in days. Determine the number of people to become infected in next 6 days.
  3. A logistics company charges a base fee of 50 dollars and additional charges of 0.5 dollars per mile for transporting goods. If a shipment travels 250 miles, what is the total cost?