SP 24 Final Exam

Front

What is the definition of inverse functions?

Back

Inverse functions are two functions, f(x) and g(x), such that f(g(x)) = x and g(f(x)) = x for all x in the domain of g and f, respectively.

Front

What does f(g(x)) represent when f and g are inverse functions?

Back

f(g(x)) is equivalent to x, meaning that applying g to x and then applying f returns the original value x.

Front

How do you identify the vertex of a quadratic function in standard form?

Back

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the Axis of Symmetry in a quadratic function?

Back

The Axis of Symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is all positive real numbers, meaning x > 0.

Front

How do you find the composition of two functions, f(g(x))?

Back

To find f(g(x)), substitute g(x) into the function f wherever x appears.

Front

What is the range of a quadratic function?

Back

The range of a quadratic function opens upwards is [k, ∞) if the vertex is (h, k) and opens downwards is (-∞, k] if the vertex is (h, k).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.

Front

What is the formula for the vertex of a parabola given in vertex form?

Back

The vertex form of a parabola is f(x) = a(x-h)^2 + k, where (h, k) is the vertex.

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, meaning f(a) = f(b) implies a = b.