Algebra 1 Lessons 3.1-3.5 Functions Test

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.

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 include quadratic, exponential, and other types of functions.

To evaluate a function at a specific point, substitute the value of the variable into the function's equation and simplify.

The range of a set of ordered pairs is the set of all second elements (y-values) from each ordered pair.

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

A function is defined for a particular input if there is a corresponding output value. If no output exists for an input, the function is undefined at that point.

The slope-intercept form of a linear equation is $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

A function is linear if its graph is a straight line. If the graph curves or has bends, it is nonlinear.

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

An example of a nonlinear function is $$f(x) = x^2$$ , which represents a parabola.