What is the parent function of h(x) = -x^2? Is it h(x) = x^2 or h(x) = -x^2?
How can I describe h(x) = -x^3 as a transformation of the parent function of a cubic function? Do I just say that it is a reflection, or is there a way of saying it with numbers, as in h(x) = x^3 - 4?
The parent function of h(x) = -x^2 is indeed h(x) = x^2. The negative sign in front of the x^2 term indicates a reflection about the x-axis compared to the parent function.
To describe h(x) = -x^3 as a transformation of the parent function of a cubic function, you can say that it is a reflection about the y-axis. This means that the entire graph of the cubic function is flipped horizontally. However, you cannot describe it as h(x) = x^3 - 4, because this expression represents a vertical shift downward by 4 units, not a reflection.
The parent function of h(x) = -x^2 is actually h(x) = x^2. The negative sign in front of the x^2 term indicates a reflection of the parent function, h(x) = x^2, across the x-axis. This means that the graph of h(x) = -x^2 is an upside-down version of the graph of h(x) = x^2.
As for describing h(x) = -x^3 as a transformation of the parent function of a cubic function, you can indeed say that it is a reflection, but you can also describe it using numbers. The parent function of a cubic function is f(x) = x^3. To reflect it across the x-axis, you can multiply the parent function by -1, resulting in h(x) = -x^3. This means that the graph of h(x) = -x^3 is a reflection of the graph of f(x) = x^3.
Alternatively, if you want to describe a different transformation, such as a vertical shift down by 4 units, you could say h(x) = x^3 - 4. This equation states that the graph of h(x) = -x^3 has been shifted downward by four units compared to the parent function f(x) = x^3.