Relations, Functions, and Zeros

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, typically representing a relationship between two sets of values.

Front

Define a function in mathematical terms.

Back

A function is a special type of relation where each input (or domain) is associated with exactly one output (or range).

Front

What is the difference between a relation and a function?

Back

A relation can have multiple outputs for a single input, while a function must have exactly one output for each input.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by parentheses containing the input variable, e.g., f(x).

Front

What does it mean for a function to be evaluated at a certain point?

Back

Evaluating a function at a certain point means substituting the input variable with a specific value and calculating the output.

Front

What is the zero of a function?

Back

The zero of a function is the value of x for which the function's output is zero, i.e., f(x) = 0.

Front

How do you find the zeros of a linear function?

Back

To find the zeros of a linear function, set the function equal to zero and solve for x.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output when the input is zero.

Front

What is the formula for finding the slope of a linear function?

Back

The slope (m) of a linear function can be calculated using the formula m = (y2 - y1) / (x2 - x1) between two points (x1, y1) and (x2, y2).

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.