Shifted hyperbolas
Move the hyperbola with b and c, read the asymptotes, D and W, and calculate the y-axis intercept.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
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Guide
The function f(x) = a/(x + b) + c is a shifted hyperbola. Its Definitionsmenge is D = ℝ \ {–b}, its Wertemenge W = ℝ \ {c}.
The graph has two asymptotes: the vertical line x = –b and the horizontal line y = c. Indirect proportionality y = k/x is the special case b = 0 and c = 0.
Zero and y-axis intercept are calculated: f(x) = 0 gives the zero, f(0) the y-axis intercept.