Semester Exam PreCal (fall)

Front

Why do rational functions have domain restrictions?

Back

Rational functions have domain restrictions because you can't divide by zero.

Front

What is a Vertical Asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

What is the range of a parabola that opens upwards?

Back

The range of a parabola that opens upwards is y ≥ k, where k is the minimum value of the function.

Front

Identify the point(s) of discontinuity at the hole for the function f(x) = \frac{x+2}{(x-3)(x+2)}.

Back

The point of discontinuity at the hole is x = -2.

Front

Factor the expression 4x^2 - 25.

Back

The factored form is (2x + 5)(2x - 5).

Front

What is the definition of a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials.

Front

What is the significance of holes in a rational function?

Back

Holes indicate points where the function is not defined due to common factors in the numerator and denominator.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes are found by setting the denominator equal to zero and solving for x.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, holes, or jumps in its graph.