Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is a linear function?

1. A function that creates a curve when graphed

2. A function that creates a straight line when graphed

3. A function that has no defined slope

4. A function with variable outputs for a constant input

The correct answer is: A function that creates a straight line when graphed

A linear function is defined as a function that creates a straight line when graphed. This characteristic is due to its mathematical representation, which is typically in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The key feature of linear functions is that they exhibit a constant rate of change; as the input value increases or decreases, the output value changes consistently, forming a straight line. This consistency in the rate of change is crucial, as it allows for predictable outcomes based on the input values. The graph does not curve, which distinguishes linear functions from nonlinear functions that do display curvature or varying rates of change. In contrast to the other choices, which describe different types of functions or characteristics, the correct choice succinctly captures the essence of a linear function in both its definition and graphical representation.