Question

question 2
the minimum point on the graph of the equation ( y = f(x) ) is ( (-1, -3) ). what is the minimum point on the graph of the equation ( y = f(x) + 5 )?
(1) ( (-1, 2) ) (2) ( (-1, -8) ) (3) ( (4, 3) ) (4) ( (-6, -3) )
answer:

Explanation:

Step1: Analyze the transformation

For the function \(y = f(x)+k\), when \(k = 5\), it is a vertical translation. The \(x -\)coordinate of the minimum point remains unchanged because there is no horizontal transformation (\(y=f(x)+5\) is of the form \(y = f(x)+k\) where \(k\) affects the \(y -\)value).

Step2: Calculate the new \(y -\)coordinate

The original \(y -\)coordinate of the minimum point is \(y=-3\). For the function \(y=f(x)+5\), we use the formula \(y_{new}=y_{old}+5\). Substitute \(y_{old}=-3\) into the formula: \(y_{new}=-3 + 5\).

$$y_{new}=2$$

Answer:

1. \((-1,2)\)