Exploring Power Functions and Their Properties

This video tutorial covers the concept of power functions, explaining their structure and properties. It distinguishes power functions from exponential functions and discusses different definitions, including those with and without coefficients. The tutorial also explores graphing power functions, highlighting the effects of positive and negative exponents and coefficients. Viewers are encouraged to explore further using graphing software like Desmos.

What is the general form of a power function?

• f(x) = a * x^k

• f(x) = k * a^x

• f(x) = x^k * a

• f(x) = k * x^a

In a power function, what is being raised to a power?

• Both the coefficient and the variable

• The variable

• Neither the coefficient nor the variable

• The coefficient

How does an exponential function differ from a power function?

• In an exponential function, the variable is raised to a constant power.

• In an exponential function, a constant is raised to the power of a variable.

• In an exponential function, both the variable and the constant are raised to powers.

• In an exponential function, neither the variable nor the constant is raised to a power.

What happens to the coefficient in a power function when evaluating it?

• It is subtracted from the result of the variable raised to the power.

• It is raised to the power of the variable.

• It is added to the result of the variable raised to the power.

• It is multiplied by the result of the variable raised to the power.

What is the shape of the graph of a power function with a positive even exponent?

• Logarithmic

• Exponential

• Parabolic

• Linear

Which points do power functions with positive even exponents and coefficients of 1 intersect?

• (0, 0) and (1, 1)

• (1, 1) and (-1, 1)

• (0, 1) and (1, -1)

• (1, 0) and (-1, 0)

What effect does multiplying a power function by a negative coefficient have on its graph?

• It reflects the graph over the x-axis.

• It reflects the graph over the y-axis.

• It shifts the graph to the left.

• It shifts the graph to the right.

What is the shape of the graph of the power function f(x) = x^3?

• Parabolic

• Linear

• Exponential

• Cubic

What happens to the graph of a power function with a negative exponent?

• It becomes a parabola.

• It becomes a straight line.

• It has a horizontal asymptote at y = 0.

• It has a vertical asymptote at x = 0.

Which graphing software is recommended for exploring power functions?

• GraphCalc

• WolframAlpha

• Desmos

• GeoGebra