Functions and Relations- A.7

Front

What is the domain in inequality notation?

Back

The domain in inequality notation represents the set of all possible input values (x-values) for a function. For example, -2 ≤ x ≤ 2 indicates that x can take any value from -2 to 2, inclusive.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept of a linear equation, set y = 0 and solve for x. For example, in the equation 3x + 8y = 24, setting y = 0 gives x = 8, so the x-intercept is (8, 0).

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, if a graph shows all y-values from negative infinity to positive infinity, the range is all real numbers.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation, set x = 0 and solve for y. For example, in the equation 4x - 10y = 20, setting x = 0 gives y = -2, so the y-intercept is (0, -2).

Front

What is the definition of a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value). This means that for each value of x, there is one and only one corresponding value of y.

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. This means that each output is produced by only one input.

Front

What is a linear function?

Back

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

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction. It is calculated as the change in y divided by the change in x (rise/run). A positive slope means the line rises, while a negative slope means it falls.

Front

What is the difference between a relation and a function?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

How do you determine if a relation is a function using the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the relation is not a function.