Function Translations and Question 24 Review

Vocabulary and core transformation concepts covering Question 24 from the lecture.

Horizontal translation to the right

A transformation of a function $y = f(x)$ where the graph shifts $h$ units to the right, represented algebraically by substituting $x - h$ for $x$, resulting in $y = f(x - h)$.

Vertical translation downward

A transformation of a function $y = f(x)$ where the graph shifts $k$ units down, represented algebraically by subtracting $k$ from the function, resulting in $y = f(x) - k$.

Equation of $g(x)$ (Question 24)

$g(x) = \frac{a - 19}{x - 4} + 2$, produced by translating $f(x) = \frac{a - 19}{x} + 5$ down by $3$ units ($5 - 3 = 2$) and right by $4$ units ($x$ replaced by $x - 4$).