1) What is a function? a) A relation between sets where each element in the domain maps to a unique element in the codomain. b) A random collection of numbers. c) A set of ordered pairs. d) A graphical representation of data points. 2) What is the domain of a function? a) The set of all possible output values. b) The set of integers. c) The set of all possible input values. d) The set of real numbers. 3) Which of the following is a rational function? a) f(x) = √x b) f(x) = 2x3 + 5x2 - 3x + 1 c) 1/x 4) What is the inverse function of f(x) = 3x - 2? a) f^(-1)(x) = (x + 2)/3 b) f^(-1)(x) = 3x + 2 c) f^(-1)(x) = 2x - 3 d) f^(-1)(x) = (x - 2)/3 5) Solve for x in the equation 2^x = 16. a) x = 4 b) x = 3 c) x = 2 d) x = 5 6) Which of the following is the exponential function? a) f(x) = log(x) b) f(x) = 1/x c) f(x) = x d) f(x) = e2 7) What is the logarithm base for the natural logarithm, ln(x)? a) 10 b) e c) 1 d) 100 8) The graph of which function will never touch the x-axis? a) f(x) = x3 - 3x2+ 2x b) f(x) = 2x2 - 4x + 2 c) f(x) = x4 + 2x2 + 1 d) f(x) = 4x3 - 6x 9) What is the range of the function g(x) = 1/(x - 2)? a) All real numbers b) All real numbers except 2 c) All positive real numbers d) All negative real numbers 10) Evaluate log2(8). a) 1 b) 2 c) 3 d) 4 11) What is a rational function? a) A function that involves only rational numbers. b) A function that is the ratio of two polynomials. c) A function that involves irrational numbers. d) A function with no defined domain. 12) What is the characteristic feature of a rational function? a) It has a finite domain. b) It has a vertical asymptote. c) It has a horizontal asymptote. d) It has no asymptotes. 13) What is an exponential function? a) A function where the variable is in the exponent. b) A function that is continuous and smooth. c) A linear function. d) A function without variables. 14) What is the general form of an exponential function? a) f(x) = ax, where a is a constant and x is the variable. b) f(x) = xa, where a is a constant and x is the variable. c) f(x) = a * x, where a is a constant and x is the variable. d) f(x) = a + x, where a is a constant and x is the variable. 15) What is a logarithmic function? a) A function that is the inverse of an exponential function. b) A function with only even exponents. c) A function that is continuous and smooth. d) A linear function. 16) What is the general form of a logarithmic function? a) f(x) = log_x(a), where a is a constant and x is the variable. b) f(x) = x^log_a(a), where a is a constant and x is the variable. c) f(x) = log_a(x), where a is a constant and x is the variable. d) f(x) = log_a(a^x), where a is a constant and x is the variable. 17) In a function, which of the following is related to the domain? a) Outputs b) Inputs c) Range d) Coefficients 18) What does the vertical line test determine about a graph? a) If the graph is increasing or decreasing b) If the graph is a function c) If the graph is a straight line d) If the graph is continuous 19) A rational function is defined as the ratio of two: a) Integers b) Fractions c) Polynomials d) Exponents 20) In a rational function, what values should be avoided for the denominator to prevent division by zero? a) Real numbers b) Complex numbers c) Imaginary numbers d) Zeros of the denominator 21) What is a one-to-one function? a) A function with multiple outputs for each input b) A function with a single output for each input c) A function with no outputs d) A function with no inputs 22) An inverse function "undoes" the actions of the original function. What does this mean? a) It reverses the operations of the original function b) It performs the same operations as the original function c) It squares the values of the original function d) It multiplies the values of the original function by 2 23) Exponential functions often represent: a) Linear growth b) Exponential growth c) Quadratic growth d) No growth at all 24) The logarithmic function is the inverse of which function? a) Linear function b) Exponential function c) Polynomial function d) Trigonometric function 25) In an exponential function, what is the variable typically used for the base? a) x b) y c) a d) c

MAT101 (General Mathematics)

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