Question

function transformation
if ((-1, 3)) is a point on the graph of (f(x)), identify which of the following ordered pairs must also be on the graph of (y = f(x) - 4)?
identify which point is on (y = f(x) - 4)
plot both points below
(circ) ((0, -4))
(circ) ((-5, 3))
(circ) ((3, 3))
(circ) ((-1, -1))

Explanation:

Step1: Recall vertical shift rule

For a function transformation \( y = f(x) + k \), if \( k < 0 \), it's a vertical shift down by \( |k| \) units. Here, \( y = f(x)-4 \), so \( k=-4 \), meaning we shift the point \((-1, 3)\) down 4 units.

Step2: Apply vertical shift to the point

The \( x \)-coordinate remains the same (\( x = -1 \)), and the \( y \)-coordinate is \( 3 - 4=-1 \). So the new point is \((-1, -1)\).

Answer:

\((-1, -1)\) (corresponding to the option \(\boldsymbol{(-1, -1)}\))