Question

which transformations to the graph of $j(x)$ would result in the graph of $j(4x)-27$?- horizontal stretch by a factor of 4, and a translation 27 units right- horizontal stretch by a factor of 4, and a translation 27 units down- horizontal compression by a factor of $\frac{1}{4}$, and a translation 27 units right- horizontal compression by a factor of $\frac{1}{4}$, and a translation 27 units down

Explanation:

For a function transformation of the form $j(kx) + c$:

1. When $|k|>1$, it creates a horizontal compression of the parent function $j(x)$ by a factor of $\frac{1}{k}$. Here, $k=4$, so it's a horizontal compression by $\frac{1}{4}$.
2. When $c$ is negative, it shifts the function downward by $|c|$ units. Here, $c=-27$, so it's a translation 27 units down.

Answer:

horizontal compression by a factor of $\frac{1}{4}$ , and a translation 27 units down