Understanding Power Functions and Graphical Representations Quiz

Explore power functions with these quiz questions covering forms, graphs, limits, derivatives, and more. Test your understanding now!

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What is the general form of a power function?

f(x) = x

f(x) = x^n

f(x) = a + bx

f(x) = log(x)

3 answered

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

2 answered

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

3 answered

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

3 answered

What is the derivative of the function f(x) = x^3 with respect to x?

3x^2

2x^3

2x^2

1 answered

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

2 answered

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

1 answered

What is the leading term of the function f(x) = 2x^4 + 3x^2 - 5?

2x^4

3x^2

-5

2x^4 + 3x^2

2 answered

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

2 answered

#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

2 answered

#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

1 answered

#12

What is the limit of the function f(x) = x^n as x approaches infinity, where n is a positive constant?

Infinity

Depends on the value of n

1 answered

#13

What is the limit of the function f(x) = x^(-n) as x approaches infinity, where n is a positive constant?

Infinity

Depends on the value of n

1 answered

#14

What is the limit of the function f(x) = x^(1/n) as x approaches infinity, where n is a positive constant?

Infinity

Depends on the value of n

1 answered

#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

Depends on the value of n

1 answered

Understanding Power Functions and Graphical Representations Quiz

What is the general form of a power function?

Which of the following is a characteristic of power functions?

What is the domain of the function f(x) = x^2?

Which of the following is a possible range for the function f(x) = x^3?

What is the derivative of the function f(x) = x^3 with respect to x?

What is the degree of a power function?

Which of the following graphs represents a power function with an exponent greater than 1?

What is the leading term of the function f(x) = 2x^4 + 3x^2 - 5?

What does the end behavior of a power function with an even degree indicate?

What is the graph of the function f(x) = x^(-2)?

What happens to the graph of a power function as the exponent approaches infinity?

What is the limit of the function f(x) = x^n as x approaches infinity, where n is a positive constant?

What is the limit of the function f(x) = x^(-n) as x approaches infinity, where n is a positive constant?

What is the limit of the function f(x) = x^(1/n) as x approaches infinity, where n is a positive constant?

What is the limit of the function f(x) = x^(-n) as x approaches 0 from the right, where n is a positive constant?

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