Function Word Problems

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value, indicating how steep the line is.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

How can you determine the equation of a line from a graph?

Back

To determine the equation, identify the slope and the y-intercept from the graph, then use the slope-intercept form y = mx + b.

Front

What is the significance of the coefficient of x in the equation y = mx + b?

Back

The coefficient of x (m) represents the slope of the line, indicating how much y changes for a unit change in x.

Front

What is the process to complete a table of values for a linear function?

Back

To complete a table of values, choose several x-values, substitute them into the function to find corresponding y-values, and fill in the table.