Graphing Higher-Degree Functions: Domain, Range, and Extrema

Professor Dave explains graphing functions, starting with basic linear functions and moving to higher degree functions like parabolas and cubic functions. He discusses the concepts of domain and range, including exceptions like vertical lines and asymptotes. The video also covers identifying relative maxima and minima, providing a comprehensive overview of graphing functions in algebra.

What is the result of F(x) when x equals 1 for the function F(x) = 2x + 1?

• 5

• 4

• 2

• 3

What shape does the graph of F(x) = x^2 represent?

• Circle

• Parabola

• Line

• Hyperbola

What happens to the value of F(x) = x^3 when x is negative?

• Becomes positive

• Becomes negative

• Becomes zero

• Remains unchanged

Which function's graph goes to positive infinity as x approaches both negative and positive infinity?

• 1/x

• x^3

• x^4

• x^2

Which function will resemble the behavior of x^3 when the exponent is odd?

• 1/x

• x^4

• x^5

• x^2

What is the domain typically like for most polynomial functions?

• Only negative numbers

• Only positive numbers

• No real numbers

• All real numbers

What causes a function to have asymptotes?

• Linear equation

• High degree polynomial

• Zero in the denominator

• Zero in the numerator

What is the range of the function F(x) = x^2?

• All real numbers

• Non-negative numbers

• All positive numbers

• Negative numbers

What type of function has a range of only one value?

• x^2

• x^3

• Horizontal line

• Vertical line

What describes a relative maximum in a function's graph?

• Point increasing to decreasing

• Point decreasing to increasing

• Lowest point on the graph

• Highest point on the graph