Final answer:
To stretch the function f(x) = √(4x) horizontally by 2, one modifies the input to f(x) = √(2x), which reflects the horizontal stretch on the graph. The concept of stretching also applies in other mathematical contexts such as exponent rules and geometric scaling.
Step-by-step explanation:
To stretch the function f(x) = √(4x) horizontally by a factor of 2, you alter the argument of the function to account for the stretching effect. Normally, horizontal stretching involves dividing the input x by the stretch factor, in this case, 2. Therefore, the horizontally stretched function would be written as f(x) = √(4(½)x) or simplified to f(x) = √(2x). This transformation affects the way the graph of the function is drawn and its interaction with the x-axis.
Additionally, understanding the properties of exponents and roots is key in working with stretches. For example, as learned from a rule in exponents, given 5¹ · 5¹, you would add the exponents to get the tidy sum of 1, yielding 5. And if we consider x², it can be re-expressed in terms of radicals as √x because squaring the square root of x gives back x, indicating how exponents relate to their roots.
In problems involving scaling, such as resizing geometric shapes, understanding that the side length of a larger square is twice the original after scaling by a factor of 2 is important. This means that a side length of 4 inches will become 8 inches after the scaling, illustrating the practical application of stretching or scaling functions in geometry.