domain, range and slope of a line

Front

What is the definition of 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.

Front

What is the definition of 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.

Front

How do you determine the slope of a line?

Back

The slope of a line is determined by the formula: slope (m) = (change in y) / (change in x) or m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal and there is no change in y as x changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it does not have a defined slope because the change in x is zero.

Front

What is the slope of the line passing through the points (1,4) and (1,-3)?

Back

The slope is undefined because the x-coordinates are the same, leading to a division by zero.

Front

What is the relationship between the slope and the steepness of a line?

Back

The greater the absolute value of the slope, the steeper the line. A positive slope rises from left to right, while a negative slope falls.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, since the function is undefined at that point.

Front

What is the range of the function f(x) = x^2?

Back

The range is all real numbers greater than or equal to 0, since the output of x^2 is never negative.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value). This can be checked using the vertical line test.