3A STARK RETEST: Unit 3 Part 2

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the domain of a function represent?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What does the range of a function represent?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine the slope of a linear function from a graph?

Back

The slope (m) of a linear function can be determined by taking two points on the line (x1, y1) and (x2, y2) and using the formula m = (y2 - y1) / (x2 - x1).

Front

What is a y-intercept?

Back

The y-intercept is the point where the graph of a function intersects the y-axis. It is represented by the value of f(0).

Front

What is the significance of a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) equals zero. It represents the x-coordinate where the graph intersects the x-axis.

Front

What is the relationship between the domain and range in a linear function?

Back

In a linear function, the domain and range are both typically all real numbers, but they can be restricted based on the context of the problem.

Front

How do you express the domain of a function using set notation?

Back

The domain can be expressed in set notation as {x | condition}, where 'condition' describes the values that x can take.

Front

What is the difference between open and closed intervals in the context of domain?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).

Front

How do you write an inequality to represent a domain?

Back

An inequality can represent a domain by indicating the range of x-values that are valid, such as @@a eq x eq b@@.