thursday review

Front

What is a function?

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 is the equation of a linear function?

Back

A linear function can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the average rate of change?

Back

The average rate of change of a function over an interval is calculated as (f(b) - f(a)) / (b - a), where a and b are the endpoints of the interval.

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

How do you calculate the slope of a line?

Back

The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is calculated as m = (y2 - y1) / (x2 - x1).

Front

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

Back

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

Front

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

Back

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

Front

What does it mean for a function to be linear?

Back

A linear function is one that graphs to a straight line, meaning it has a constant rate of change.

Front

How can you determine if a relation is a function from a graph?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (often x), while the dependent variable is the output (often y) that depends on the input.