Algebra 2/Trig Chapter 1 Review

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a graph, or an equation.

Front

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

Back

A function is one-to-one if it assigns different outputs to different inputs, meaning no two different inputs produce the same output.

Front

What is the definition of an even function?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain of f. Its graph is symmetric about the y-axis.

Front

What is the definition of an odd function?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f. Its graph is symmetric about the origin.

Front

How do you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h) for the quadratic f(x) = ax² + bx + c.

Front

What is the relationship between the roots and the coefficients of a polynomial?

Back

For a quadratic polynomial ax² + bx + c, the sum of the roots is -b/a and the product of the roots is c/a.