Reading f(x). Composition. Shifts, stretches, reflections.
f(x) is just a rule. f(3) means "plug 3 in for x". The output is whatever the rule gives back.
Composition f(g(x)): apply g first, then feed the result into f.
Transformations of y = f(x):
y = f(x − h) — shifts the graph right by h (counter-intuitive — minus inside means right).y = f(x) + k — shifts up by k.y = a · f(x) — vertical stretch by |a|; flips if a < 0.y = f(−x) — reflects across the y-axis.y = −f(x) — reflects across the x-axis.A function is even if f(−x) = f(x) (mirror symmetry across the y-axis), and odd if f(−x) = −f(x) (180° rotational symmetry about the origin).
f(x) = x² − 1, find f(3) and f(−2).f(3) = 3² − 1 = 9 − 1 = 8f(−2) = (−2)² − 1 = 4 − 1 = 3f(x) = x² and g(x) = 2x + 1, find f(g(2)).g(2) = 2(2) + 1 = 5f(5) = 5² = 258 questions on evaluating functions, composition, and identifying transformations.