Answer:
46 degrees
Explanation:
Certainly, let's provide a mathematical explanation for the transformation of the function from f(x) to h(x).
The original function is given as:
f(x) = (x + 2)³ - 3
Horizontal Shift: The term "(x + 2)" represents a horizontal shift to the left by 2 units. This means that every point on the graph of f(x) is moved 2 units to the left compared to the standard cubic function.
Cubic Function: The term "³" represents a cubic function. It indicates that the graph is a cubic curve, which has a characteristic shape with a single point of inflection.
Vertical Shift: The term "-3" represents a vertical shift downward by 3 units. This means that the entire graph is shifted downward by 3 units compared to the standard cubic function.
Now, to express h(x) in terms of x, we perform the same transformations on a basic cubic function, which we'll call k(x):
k(x) = x³
To obtain h(x), we apply the same transformations to k(x):
h(x) = k(x + 2) - 3
This expression for h(x) mirrors the transformations applied to the original function f(x). It represents a cubic function that has been shifted 2 units to the left and 3 units down from the standard cubic function.
So, h(x) = (x + 2)³ - 3 is the expression for h(x) that matches the transformations applied to f(x).