Chapter 2 Flashcard Algebra II

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, for the function f(x) = x^2, the range is [0, infinity) because the output is always non-negative.

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. For example, for the function f(x) = 1/x, the domain is all real numbers except x = 0.

Front

Given the function f(x) = x^2 - 6x + 8, what is the range?

Back

The range is [0, infinity) because the vertex of the parabola is at (3, -1) and opens upwards.

Front

Given the function f(x) = -x^2 + 4, what is the range?

Back

The range is (-infinity, 4] because the vertex is at (0, 4) and the parabola opens downwards.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. This means that for every x in the domain, f(x) is defined and the limit as x approaches a value equals the function's value at that point.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different parts of its domain. For example, f(x) = { x^2 for x < 0; x + 2 for x >= 0 }.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

How do you find the domain of a rational function?

Back

To find the domain of a rational function, identify values of x that make the denominator zero, as these values are excluded from the domain.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, the curve is not a function.

Front

What is a function's inverse?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(x) = y, then the inverse function f^(-1)(y) = x.