Understanding Polynomial Functions and Their Graphs

Why is it often desirable to sketch a quick representation of a polynomial function's graph?

• To create a detailed and accurate graph

• To avoid using graphing utilities

• To find the exact roots of the function

• To get a general idea of the function's behavior

What is a characteristic of a continuous graph?

• It is only defined for positive x values

• It has sharp corners

• It can be drawn without lifting the pen

• It has breaks and jumps

Which of the following is an example of a discontinuous function?

• x squared

• x cubed

• x plus 2

• 1 over x

What does it mean for a graph to be smooth?

• It has no sharp corners

• It is only defined for positive x values

• It has breaks and jumps

• It can be drawn without lifting the pen

Why is the graph of the absolute value of x not considered smooth?

• It is not continuous

• It has a sharp corner at the origin

• It has a break at the origin

• It is not defined for negative x values

What is the domain of polynomial functions?

• All negative real numbers

• All positive real numbers

• All integers

• All real numbers

What are the x-intercepts of a polynomial function's graph also known as?

• Slopes

• Zeros

• Valleys

• Peaks

What is the zero product property used for?

• Sketching the graph of a function

• Finding the slope of a graph

• Determining the continuity of a function

• Finding the roots of a polynomial

Which method can be used to find the roots of a quadratic equation when factoring is difficult?

• Graphing

• Completing the square

• Quadratic formula

• Trial and error

What is a common factor in the polynomial x-cubed plus x-squared minus two x?

• x minus 2

• x plus 1

• x

• x squared