Functions and Graphical Analysis Quiz
Test your understanding of functions, limits, derivatives, and integrals with this calculus quiz on graphical analysis.
#1
Which of the following best defines a function in mathematics?
A set of ordered pairs where each input has exactly one output
A mathematical expression with only constants
A graph with no x-intercepts
A set of equations with multiple solutions
#2
What does the vertical line test determine about a graph?
Whether a function is increasing or decreasing
Whether a function has a maximum or minimum value
Whether a graph represents a function
Whether a graph is symmetrical
#3
What is the inverse of the function f(x) = 2x + 3?
f^(-1)(x) = (x - 3) / 2
f^(-1)(x) = (x + 3) / 2
f^(-1)(x) = (x - 3) * 2
f^(-1)(x) = (x + 3) * 2
#4
What are the critical points of a function?
Points where the function has a critical value
Points where the function is not defined
Points where the function changes direction or has a local maximum or minimum
Points where the function intersects the x-axis
#5
What is the limit of the function f(x) = 1/x as x approaches infinity?
#6
Which of the following functions is odd?
f(x) = x^2 - 2x + 1
f(x) = x^3 - 3x
f(x) = x^4 + 2x^3 - x^2 + 3
f(x) = x^5 + x^3 - x
#7
What is the domain of the function f(x) = sqrt(x - 3)?
All real numbers
x > 3
x < 3
x >= 3
#8
What does it mean for a function to be concave up?
The function has a positive slope
The function has a negative slope
The function is always increasing
The function curves upward like a cup
#9
What is the inflection point of a function?
The point where the function intersects the x-axis
The point where the function has a maximum or minimum value
The point where the function changes concavity
The point where the function is not defined
#10
What does the second derivative of a function indicate about its behavior?
The rate of change of the function
The concavity of the function
The maximum value of the function
The inflection points of the function
#11
What is the area under the curve of a function within a specific interval called?
The derivative
The integral
The limit
The critical point
#12
Which of the following statements is true for even functions?
They have symmetry about the y-axis
They have symmetry about the x-axis
They pass through the origin
They have no symmetry
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