Determining Equations of Hyperbola Graphs

This question requires learners to determine the equations of hyperbolic functions of the forms

𝑓
(
𝑥
)
=
𝑎
𝑥
+
𝑞
and
𝑔
(
𝑥
)
=
𝑎
𝑥
+
𝑝
+
𝑞
.
f(x)=
x
a
​

+qandg(x)=
x+p
a
​

+q.

Using the given asymptotes and points on each graph, learners identify horizontal and vertical shifts as well as the value of
𝑎
a. The task develops understanding of transformations of the basic reciprocal function and how graphical features translate into algebraic equations.

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