Precalc. AB Semester Final Part 1

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions where the output of one function becomes the input of another. It is denoted as (g ∘ f)(x) = g(f(x)).

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is the solution set for the inequality x^2 - 2x - 3 ≤ 0?

Back

Front

How do you express exponential decay mathematically?

Back

Exponential decay can be expressed as m(t) = m_0 * (1 - r)^t, where m_0 is the initial amount, r is the decay rate, and t is time.

Front

What is the domain of the function f(x) = (x - 1) / (x^2 - 25)?

Back

Front

What is the quadratic formula?

Back

Front

What is a vertical asymptote?

Back

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

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing on an interval if its derivative is positive on that interval, and decreasing if its derivative is negative.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

Front

What is the significance of the leading coefficient in polynomial functions?

Back

The leading coefficient determines the end behavior of the polynomial function. If it is positive, the function rises to the right; if negative, it falls to the right.