Final answer:
To graph the function f(x) = 3x + 4, plot the y-intercept and use the slope to draw the line. Find the inverse function by swapping x and y in the equation and solving for y, then graph it similarly. Both lines are straight and inverse functions are reflected across the line y = x.
Step-by-step explanation:
To graph the function f(x) = 3x + 4, you would plot the y-intercept at (0, 4) and then use the slope (which is 3) to find another point. Since the slope is 3, it means for each step right on the x-axis, you go up 3 units on the y-axis. After plotting at least two points, you can draw a straight line through these points to extend the graph of f(x).
The inverse function, on the other hand, is a separate consideration. However, the value given, f¹(2) = 234, is likely an error, because this does not follow from the inverse of f(x). The inverse function of f(x) = 3x + 4 would be found by swapping x and y and solving for y. The equation would then be x = 3y + 4, which simplifies to f¹(x) = (x - 4) / 3. To graph this, you'd start with the x-intercept at (4,0) and the slope of 1/3, indicating that for every 3 units right on the x-axis, you go up 1 unit on the y-axis.
Both graphs will be straight lines and since they are inverse functions, they will be reflections of each other across the line y = x. When drawing these functions, it is important to label each line clearly with its corresponding equation and to choose an appropriate scale for both x and y axes, based on the maximum and minimum values you need to plot.