#1
Which of the following best defines a function in mathematics?
A set of ordered pairs where each input has exactly one output
ExplanationFunctions map each input to exactly one output.
#2
What does the vertical line test determine about a graph?
Whether a graph represents a function
ExplanationA graph passes the vertical line test if it intersects any vertical line at most once, indicating it represents a function.
#3
What is the inverse of the function f(x) = 2x + 3?
f^(-1)(x) = (x - 3) / 2
ExplanationThe inverse function swaps input and output values.
#4
What are the critical points of a function?
Points where the function changes direction or has a local maximum or minimum
ExplanationCritical points are where the derivative is zero or undefined.
#5
What is the limit of the function f(x) = 1/x as x approaches infinity?
0
ExplanationThe function approaches zero as x approaches infinity.
#6
Which of the following functions is odd?
f(x) = x^3 - 3x
ExplanationOdd functions have rotational symmetry about the origin.
#7
What is the domain of the function f(x) = sqrt(x - 3)?
x >= 3
ExplanationThe domain of a square root function excludes negative values.
#8
What does it mean for a function to be concave up?
The function curves upward like a cup
ExplanationConcave up indicates the function is curving upwards.
#9
What is the inflection point of a function?
The point where the function changes concavity
ExplanationInflection points are where the concavity changes.
#10
What does the second derivative of a function indicate about its behavior?
The concavity of the function
ExplanationSecond derivative helps identify concavity changes.
#11
What is the area under the curve of a function within a specific interval called?
The integral
ExplanationIntegration finds the area under curves.
#12
Which of the following statements is true for even functions?
They have symmetry about the y-axis
ExplanationEven functions exhibit reflectional symmetry about the y-axis.