Questions: Consider the following function. r(x) = x^2/4 - 3 Step 1 of 4: Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer f(x) =

Solution Steps

To determine the more basic function that has been transformed, we need to identify the core function before any transformations. The given function \( r(x) = \frac{x^2}{4} - 3 \) is a transformation of the basic quadratic function \( f(x) = x^2 \). The transformations include a vertical compression by a factor of 1/4 and a vertical shift downward by 3 units.

The given function is \( r(x) = \frac{x^2}{4} - 3 \). The basic function from which this is derived is the quadratic function \( f(x) = x^2 \).

The function \( r(x) \) is a transformation of \( f(x) = x^2 \). The transformations applied are:

• A vertical compression by a factor of \(\frac{1}{4}\), resulting in \(\frac{x^2}{4}\).
• A vertical shift downward by 3 units, resulting in \(\frac{x^2}{4} - 3\).

Final Answer