#1
What is the general form of a power function?
f(x) = x^n
ExplanationGeneral form of a power function.
#2
Which of the following is a characteristic of power functions?
They exhibit exponential growth or decay
ExplanationCharacteristic of power functions.
#3
What is the domain of the function f(x) = x^2?
All real numbers
ExplanationDomain of a specific power function.
#4
Which of the following is a possible range for the function f(x) = x^3?
All real numbers
ExplanationPossible range of a specific power function.
#5
What is the derivative of the function f(x) = x^3 with respect to x?
3x^2
ExplanationDerivative of a specific power function.
#6
What is the degree of a power function?
The highest power of the variable in the function
ExplanationDegree of a power function.
#7
Which of the following graphs represents a power function with an exponent greater than 1?
A curve starting from the origin and bending upwards
ExplanationGraph of a power function with exponent > 1.
#8
What is the leading term of the function f(x) = 2x^4 + 3x^2 - 5?
2x^4
ExplanationLeading term of a polynomial function.
#9
What does the end behavior of a power function with an even degree indicate?
Both ends of the graph point in the same direction
ExplanationEnd behavior of power function with even degree.
#10
What is the graph of the function f(x) = x^(-2)?
A hyperbola opening downwards
ExplanationGraph of a power function with a negative exponent.
#11
What happens to the graph of a power function as the exponent approaches infinity?
The graph flattens out
ExplanationBehavior of the graph as the exponent approaches infinity.
#12
What is the limit of the function f(x) = x^n as x approaches infinity, where n is a positive constant?
Infinity
ExplanationLimit of a power function as x approaches infinity.
#13
What is the limit of the function f(x) = x^(-n) as x approaches infinity, where n is a positive constant?
0
ExplanationLimit of a power function with negative exponent.
#14
What is the limit of the function f(x) = x^(1/n) as x approaches infinity, where n is a positive constant?
Infinity
ExplanationLimit of a power function with fractional exponent as x approaches infinity.
#15
What is the limit of the function f(x) = x^(-n) as x approaches 0 from the right, where n is a positive constant?
Infinity
ExplanationLimit of a power function with negative exponent as x approaches 0 from the right.