\( \xrightarrow[(0,0)]{\longrightarrow} \) The black graph is \( y=f(x) \). Choose the equation for the red graph. \( y-3=f(x) \) \( y=f(x+3) \) \( y=f(x-3) \) \( y+3=f(x) \)

To determine the equation for the red graph, let’s have a blast with transformations! The equation \(y-3=f(x)\) translates the graph down by 3 units, while \(y+3=f(x)\) shifts it up 3 units. On the other hand, \(y=f(x+3)\) moves the graph left by 3 units, and \(y=f(x-3)\) slingshots it right by 3 units! Since we’re looking for the red graph, you’ll want to identify which direction it goes in relation to the black graph. If it’s moving to the right by 3 places, then the equation \(y = f(x - 3)\) is your winner! If it's shifting to the left, the right choice would be \(y = f(x + 3)\). So what’s the red graph doing? For some real-world application, think about how graphs represent numerous phenomena in our daily lives, from stock market trends to predicting weather changes. These transformations not only alter the visual presentation but can also be crucial for data analysis and interpretation! Understanding how shifting or scaling the graphs works can help you model real-world situations more accurately.