Question

to shift the function left by 3 units, add 3 to the independent variable. to shift the function up by 4 units, add 4 to the original function.\\(g(x) = f(x + 3) + 4\\)\\(= \frac{3}{(x + 3) + 1} + 4\\)\\(= \frac{3}{x + 4} + 4\\)\part c\consider function ( h ).\\(h(x) = \frac{9}{x - 1}\\)\select the correct answer from each drop - down menu.\function ( h ) is a transformation of function ( f ), which is stretched vertically by a factor of (\boxed{}) and (\boxed{}).

Explanation:

Step1: Identify base function $f(x)$

From the earlier example, $f(x) = \frac{3}{x+1}$

Step2: Compare $h(x)$ to scaled $f(x)$

Rewrite $h(x)=\frac{9}{x-1}$ as $h(x)=3\times\frac{3}{x-1}$. Now adjust $f(x)$ to match the denominator: replace $x$ with $x-2$ in $f(x)$ to get $f(x-2)=\frac{3}{(x-2)+1}=\frac{3}{x-1}$. So $h(x)=3f(x-2)$.

Step3: Interpret transformations

A coefficient of 3 outside $f(x-2)$ means vertical stretch by 3. The $x-2$ inside $f$ means shift right 2 units.

Answer:

Function $h$ is a transformation of function $f$, which is stretched vertically by a factor of $\boldsymbol{3}$ and shifted right by 2 units