In Problems 59-70, (a) graph each function. (b) Determine...

In Problems $59-70,$ (a) graph each function. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing.
$$
f(x)=\frac{3}{2} x-2
$$

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Key Concepts

Linear Function

A linear function is a function of the first degree, typically expressed in the form f(x) = mx + b. It graphs as a straight line and exhibits a constant rate of change, making it one of the most fundamental types of functions in algebra and calculus.

Slope-Intercept Form

The slope-intercept form of a linear function (f(x) = mx + b) directly identifies two crucial features: the slope (m), which indicates the rate at which the function increases or decreases, and the y-intercept (b), which provides the point at which the line crosses the y-axis.

Domain and Range

The domain of a function is the set of all permissible input values, and the range is the set of possible output values. For linear functions without restrictions, such as those defined by f(x) = mx + b, both the domain and the range typically consist of all real numbers.

Increasing and Decreasing Behavior

The increasing or decreasing nature of a function is determined by its rate of change. In linear functions, if the slope (m) is positive, the function is increasing (outputs become larger as inputs increase). Conversely, if the slope is negative, the function is decreasing (outputs become smaller as inputs increase).

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