Intro to College Algebra Review

Front

What is the domain of the function f(x) = 1/(x+1)?

Back

The domain is all real numbers except x = -1, which can be expressed as (-∞, -1) U (-1, ∞).

Front

State the equation of a circle with center (h, k) and radius r.

Back

The equation is (x - h)² + (y - k)² = r².

Front

What is the center and radius of the circle given by the equation (x + 4)² + (y - 1)² = 16?

Back

Center = (-4, 1), Radius = 4.

Front

How do you find the product of two functions f(x) and g(x)?

Back

The product (fg)(x) is found by multiplying the two functions: (fg)(x) = f(x) * g(x).

Front

What is the radius of the circle defined by the equation (x - 3)² + (y + 5)² = 25?

Back

The radius is 5, since r² = 25.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you determine the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

The distance is given by d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.