Question

question 1 (1 point)
if any of the factors of a polynomial function are linear, then which of the following is not true?

a) the graph has a linear shape near this ( x )-intercept.

b) the ( x )-intercept is a point where the curve passes through the ( x )-axis.

c) the ( x )-axis is tangent to the curve at these points.

d) the zeros of the function are locations on the graph where ( y = 0 ).

Explanation:

• Option a: For a linear factor $(x-a)$, near $x=a$, the polynomial behaves like the linear term, so the graph has a linear shape near the intercept. This is true.
• Option b: An x-intercept is defined as the point where the graph crosses the x-axis (where $y=0$), which corresponds to the zero from the linear factor. This is true.
• Option c: The x-axis is tangent to the curve at a zero only if the factor is repeated (a multiple root). For a distinct linear factor (single root), the graph crosses the x-axis, not tangent to it. This is false.
• Option d: By definition, zeros of a function are the x-values where $y=0$, which are the x-intercepts from linear factors. This is true.

Answer:

c) The x-axis is tangent to the curve at these points.