In Problems 59-70, (a) graph each function. (b) Determine the domain and the range of the functi

step 1 We need to graph the following function and then find the information that's being asked. So we'

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

Key Concepts

Linear Functions

A linear function is a polynomial function of degree one with a constant rate of change, typically expressed in the form f(x) = mx + b, where m represents the slope and b is the y-intercept. Its graph is a straight line, making it one of the simplest types of functions to analyze in algebra.

Domain and Range

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values) that result from the function. For linear functions, the domain and range are usually all real numbers, since there are no restrictions on the values that x or f(x) can take.

Graphing Functions

Graphing a function involves plotting points on a coordinate system by substituting various x-values into the function and then connecting these points to reveal the function's behavior. In the case of a linear function, only two distinct points are needed to determine the line, because the function has a constant slope.

Increasing and Decreasing Intervals

Increasing and decreasing intervals describe portions of the function's domain where the function values either rise or fall, respectively. For a linear function, the behavior is determined by the slope: if the slope is positive, the function is increasing for all x-values; if the slope is negative, the function is decreasing for all x-values.

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