Understanding Polynomial Functions

What is the graph of a zero-degree polynomial function known as?

• A vertical line

• A sloped line

• A parabola

• A horizontal line

What is a monomial in the context of polynomials?

• A constant function

• A quadratic function

• A single term of the form 'a' times 'x to the nth power'

• A sum of multiple terms

How do graphs of monomials with even exponents behave as the exponent increases?

• They become symmetrical with respect to the origin

• They pass through the point (-1, -1)

• They become steeper between -1 and 1

• They become flatter between -1 and 1

Which point do all graphs of monomials with even exponents pass through?

• (0, 0)

• (1, 0)

• (0, 1)

• (-1, -1)

What is a key characteristic of graphs of monomials with odd exponents?

• They are symmetrical with respect to the vertical axis

• They become flatter as the exponent increases

• They are symmetrical with respect to the origin

• They pass through the point (-1, 1)

What is the primary difference between graphs of even and odd powers of x?

• Even powers are steeper

• Odd powers are symmetrical with respect to the vertical axis

• Even powers are symmetrical with respect to the vertical axis

• Odd powers pass through the point (1, 1)

What is the effect of a monomial's exponent on its graph?

• It changes the graph's horizontal position

• It influences the graph's steepness

• It affects the graph's vertical stretch

• It determines the graph's symmetry

How does increasing the coefficient of a monomial affect its graph?

• It shifts the graph horizontally

• It reflects the graph across the y-axis

• It stretches the graph vertically

• It compresses the graph horizontally

What happens to the graph of a monomial if the coefficient is negative?

• It shifts upwards

• It reflects across the x-axis

• It remains unchanged

• It becomes a horizontal line

What is the result of decreasing the coefficient of a monomial?

• The graph stretches vertically

• The graph shrinks vertically

• The graph shifts to the right

• The graph becomes a constant function