Anthony wants to draw the graph of the linear function 𝑓 of 𝑥 is equal to three 𝑥 minus four. He plotted the points with 𝑥-coordinates zero, one, two, three, and four but made one mistake. Which point is incorrect? What are the correct coordinates of this point?
We are told in the question that Anthony wanted to draw the graph of the linear function 𝑓 of 𝑥 is equal to three 𝑥 minus four. We know that any linear function is represented graphically as a straight line. Drawing a straight line that passes through points 𝐴 and 𝐸, we notice that this also passes through the points 𝐵 and 𝐶. This suggests that the point that is incorrect is point 𝐷. From the graph, this point has coordinates three, four.
We can check whether this point lies on the graph of the function 𝑓 of 𝑥 is equal to three 𝑥 minus four by substituting 𝑥 equals three into the function. 𝑓 of three is equal to three multiplied by three minus four. This is equal to nine minus four, which is equal to five. As this is not equal to four, this confirms that the point that is incorrect is point 𝐷 and the correct coordinates of this point are three, five.
At this point, it is also worth substituting the 𝑥-values of zero, one, two, and four into our function. 𝑓 of zero is equal to three multiplied by zero minus four, which is equal to negative four. 𝑓 of one is equal to negative one, 𝑓 of two is equal to two, and 𝑓 of four is equal to eight. These four values correspond to the points with coordinates zero, negative four; one, negative one; two, two; and four, eight, which are the points 𝐴, 𝐵, 𝐶, and 𝐸, respectively, on our graph. All four of these points satisfy the function 𝑓 of 𝑥 is equal to three 𝑥 minus four, which confirms that the incorrect point is point 𝐷.