#1
Which of the following is the graph of a quadratic function?
Parabola
ExplanationA quadratic function graph is represented by a parabola.
#2
What is the domain of the function f(x) = √(x - 3)?
x ≥ 3
ExplanationThe domain includes all real numbers greater than or equal to 3.
#3
Which of the following represents an exponential function?
f(x) = e^x
ExplanationAn exponential function is of the form f(x) = a^x, where a is a constant and e is the base of the natural logarithm.
#4
Which of the following represents a logarithmic function?
f(x) = log(x)
ExplanationA logarithmic function is defined as f(x) = log_b(x), where b is the base of the logarithm.
#5
Which of the following is the correct definition of a function?
A relation that assigns exactly one output to each input
ExplanationA function assigns each input exactly one output, avoiding ambiguity.
#6
Which of the following is the correct interpretation of the derivative of a function?
Instantaneous rate of change
ExplanationThe derivative of a function represents the rate of change at a particular point.
#7
What is the vertex of the function f(x) = 2x^2 + 4x - 3?
(-1, 5)
ExplanationThe vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by (-b/2a, f(-b/2a)).
#8
What is the range of the function f(x) = sin(x)?
[-1, 1]
ExplanationThe range of the sine function is bounded between -1 and 1.
#9
What is the asymptote of the function f(x) = 1/x?
x = 0
ExplanationThe function has a vertical asymptote at x = 0.
#10
What is the period of the function f(x) = cos(2x)?
2π
ExplanationThe period of the cosine function is 2π.
#11
Which of the following functions is odd?
f(x) = x^3 - x
ExplanationA function is odd if f(-x) = -f(x), which holds true for this cubic function.
#12
Which of the following functions is even?
f(x) = x^4 - 2x^2
ExplanationA function is even if f(-x) = f(x), which holds true for this quartic function.