#1
What is the general form of a power function?
f(x) = x
f(x) = x^n
f(x) = a + bx
f(x) = log(x)
#2
Which of the following is a characteristic of power functions?
They always intersect the y-axis at (0,0)
They have a constant rate of change
They exhibit exponential growth or decay
They always have a negative exponent
#3
What is the domain of the function f(x) = x^2?
All real numbers
All positive real numbers
All non-negative real numbers
All negative real numbers
#4
Which of the following is a possible range for the function f(x) = x^3?
All real numbers
All positive real numbers
All non-negative real numbers
All negative real numbers
#5
What is the derivative of the function f(x) = x^3 with respect to x?
#6
What is the degree of a power function?
The highest power of the variable in the function
The sum of the exponents in the function
The lowest power of the variable in the function
The coefficient of the highest power term
#7
Which of the following graphs represents a power function with an exponent greater than 1?
A straight line passing through the origin
A curve starting from the origin and bending upwards
A curve starting from the origin and bending downwards
A straight line not passing through the origin
#8
What is the leading term of the function f(x) = 2x^4 + 3x^2 - 5?
#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
Both ends of the graph point in opposite directions
The graph is always concave up
The graph is always concave down
#10
What is the graph of the function f(x) = x^(-2)?
A parabola opening upwards
A parabola opening downwards
A hyperbola opening upwards
A hyperbola opening downwards
#11
What happens to the graph of a power function as the exponent approaches infinity?
The graph shifts upwards
The graph shifts downwards
The graph becomes steeper
The graph flattens out
#12
What is the limit of the function f(x) = x^n as x approaches infinity, where n is a positive constant?
0
1
Infinity
Depends on the value of n
#13
What is the limit of the function f(x) = x^(-n) as x approaches infinity, where n is a positive constant?
0
1
Infinity
Depends on the value of n
#14
What is the limit of the function f(x) = x^(1/n) as x approaches infinity, where n is a positive constant?
0
1
Infinity
Depends on the value of n
#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?
0
1
Infinity
Depends on the value of n