Question

given $f(x)=x^{2}$, after performing the following transformations: shift upward 18 units and shift 15 units to the right, the new function $g(x)=$

Explanation:

Step1: Shift right transformation

For a function $y = f(x)$, shifting it $a$ units to the right gives $y=f(x - a)$. Here $a = 15$ and $f(x)=x^{2}$, so after shifting 15 units to the right, the function becomes $y=(x - 15)^{2}$.

Step2: Shift upward transformation

For a function $y = h(x)$, shifting it $b$ units upward gives $y=h(x)+b$. Here $b = 18$ and $h(x)=(x - 15)^{2}$, so after shifting 18 units upward, the new function $g(x)=(x - 15)^{2}+18$.

Answer:

$g(x)=(x - 15)^{2}+18$