Given the function , what is the new function after a horizontal stretch by a
factor of 4?
Option #1:
Option #2:
Option #3:
Option #4:

To apply a horizontal stretch by a factor of 4 to the function , we need to replace with . This gives us the new function:

So, the correct option is Option #3: .

Now that you know the answer, here’s a little extra trivia: Horizontal stretches actually affect how wide the graph appears—basically, it makes the function spread out! This means that as you move from left to right along the x-axis, the function takes longer to reach higher values, resulting in a flatter appearance.

Thinking of practical applications, functions like this pop up in various fields. For instance, in physics, the relationships between quantities often depend on such transformations. If you stretch time or space for certain events or measurements, you’re effectively applying these types of transformations to the underlying functions to model real-world behavior!