True or False. If f(x) = (x^2−16) / (x−4) and g(x) = x + 4, then we can say the functions f and g?

Answer 1

both g(x) and f(x) are the same straight line with slope = 1 and y intercept = 4

except f(x) has a hole in it, a discontinuity at the point (4,8)

Answer 2

f(x) = (x² - 16) / (x - 4) = (x + 4)(x - 4) / (x - 4) = x + 4. as long as x ≠ 4.

g(x) = x + 4

f(x) = g(x) for all x except at x = 4

The graph of g is a straight line with slope 1 and y-intercept (0,4).

The graph of f is the same as the graph of g except for a "hole" in the graph at the point (4, 8).

We say that f has a removable discontinuity when x = 4, whereas g is continuous for all x.