1st Semester - Precalculus Final Review

Front

What are the decreasing intervals on the graph?

Back

The decreasing intervals are (-∞, -2) & (2, ∞).

Front

A removable point of discontinuity is a factor that can be canceled out from the rational function. It shows up as an open circle on the graph. Its called a...

Back

hole

Front

Find the horizontal asymptote for the function. What is it?

Back

y = -1/3

Front

Determine the value of the discriminant for the quadratic equation x² + 7x + 13 and name the nature of the roots.

Back

The discriminant is -3, indicating 2 imaginary roots.

Front

If there is a turning point on the x-axis (a.k.a 'touches'), what does that mean about the multiplicity of that zero?

Back

Even

Front

What is the definition of a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: 2 real roots, 1 real root (double), or 2 imaginary roots.

Front

What is the significance of a vertical asymptote in a rational function?

Back

A vertical asymptote indicates values of x where the function approaches ±∞, typically where the denominator is zero.

Front

What does it mean if a function has a zero of odd multiplicity?

Back

A zero of odd multiplicity means the graph crosses the x-axis at that point.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.