Final answer:
The y-intercept of the function f(x) = 3x - 6 is -6, indicating the temperature at sunrise. The x-intercept is 2, showing that the temperature reaches 0°C two hours after sunrise. Plotting these intercepts and using the slope of 3 allows one to graph the linear function.
Step-by-step explanation:
The function f(x) = 3x - 6 represents the air temperature, with x being the number of hours after sunrise. The y-intercept is -6, which means that at sunrise (when x = 0), the temperature is -6°C. To find the x-intercept, we set f(x) to 0 and solve for x: 0 = 3x - 6. Adding 6 to both sides and then dividing by 3 gives us x = 2. This x-intercept means that the temperature reaches 0°C two hours after sunrise.
To graph this function, begin at the y-intercept (-6) on the y-axis. The slope of the line is 3, which means for every hour after sunrise, the temperature rises by 3°C. Starting at the y-intercept, move up 3 units and to the right 1 unit to follow the slope. Continue this pattern and draw a line through these points. The x-intercept of 2 will be where this line crosses the x-axis. This line illustrates how both b and m terms in the equation y = mx + b determine the shape of the line. b is the y-intercept and m is the slope of the line.