Unit 2B Review

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis. It is the value of y when x is 0, and can be found in the equation of the line in the form y = mx + b, where b is the y-intercept.

Front

How do you find the slope from an equation in standard form?

Back

To find the slope from an equation in standard form (Ax + By = C), rearrange it into slope-intercept form (y = mx + b) by solving for y. The coefficient of x will be the slope.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases. This is indicated by a positive slope on the graph.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (y) decreases. This is indicated by a negative slope on the graph.

Front

What is the significance of the slope in a real-world context?

Back

In real-world contexts, the slope represents the rate of change. For example, in a cost function, the slope indicates how much the total cost increases for each additional item purchased.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept represents the starting value of the dependent variable when the independent variable is zero. For example, in a cost function, it may represent a fixed fee before any items are purchased.