Final Pre-Calculus

Front

Find the x-intercept(s) of a function.

Back

The x-intercept(s) of a function are the points where the graph intersects the x-axis, meaning the output (y-value) is zero.

Front

What does the leading term of a polynomial indicate about its end behavior?

Back

The leading term's coefficient and degree determine the end behavior of the polynomial. A negative coefficient with an even degree means the ends of the graph will both point down.

Front

Factor the quadratic expression: 3x² + 5x - 12.

Back

(3x - 4)(x + 3) is the complete factorization of the expression.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the formula for the sum of the first n terms of an arithmetic series?

Back

The sum S_n of the first n terms is given by S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the difference between even and odd functions?

Back

An even function satisfies f(-x) = f(x) for all x, while an odd function satisfies f(-x) = -f(x) for all x.

Front

How do you determine the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided those values do not also make the numerator zero.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.