Flashcard 9

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 f(x) = 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 can include quadratic, exponential, and other types of functions.

Front

How can you determine if a function is linear or nonlinear from a table of values?

Back

To determine if a function is linear from a table, check if the differences between consecutive y-values are constant for equal intervals of x-values. If they are constant, the function is linear.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented as (0, b) where b is the value of the function when x = 0.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the significance of a greater rate of change in a function?

Back

A greater rate of change indicates that the function's output (y-value) increases or decreases more rapidly with respect to changes in the input (x-value), which can be important in comparing different functions.

Front

How can you identify the slope from a graph of a linear function?

Back

The slope can be identified by selecting two points on the line and using the formula (y2 - y1) / (x2 - x1) to calculate the rise over run.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What are some common forms of nonlinear functions?

Back

Common forms of nonlinear functions include quadratic functions (e.g., f(x) = ax^2 + bx + c), exponential functions (e.g., f(x) = a * b^x), and logarithmic functions.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of the input variable.