How exactly would I solve these problems?

Write a function g(x)with the given transformations of f(x)=x to the 2 power.

A. Down 2
B. reflection about the x-axis

My teacher never taught me this, and my exam is within the next 2 weeks.

well, to move the graph down two just subtract 2 from every value of f(x) to get g(x)

g(x) = x^2 - 2

now if you want to reflect about the x axis, then you want every value of g(x) to be negative the value of f(x)
so write g(x) = -f(x) whatever f(x) is
so if f(x) = x^2 - 2 for example then
g(x) = -x^2 + 2

Thank you so much. :)

To solve the given problem, you need to understand the transformations and how they affect the original function f(x). Here's how you can solve it step by step:

Step 1: Understand the original function:
The original function given is f(x) = x^2, which represents a basic quadratic function.

Step 2: Down 2 transformation:
To perform the "Down 2" transformation, you need to shift the graph of the original function downward by 2 units. This can be achieved by subtracting 2 from the original function.

g(x) = f(x) - 2
= x^2 - 2

This gives you the transformed function g(x) with the "Down 2" transformation.

Step 3: Reflection about the x-axis:
To perform the "reflection about the x-axis" transformation, you need to flip the graph of the transformed function g(x) upside down. This involves multiplying the function by -1.

g(x) = -1(x^2 - 2)
= -x^2 + 2

This gives you the final transformed function g(x) with both the "Down 2" and "reflection about the x-axis" transformations.

Now you have the function g(x) = -x^2 + 2, which represents a quadratic function transformed from the original f(x) = x^2 function.

To further familiarize yourself with this topic and gain more clarity, it is recommended to practice and solve more examples of function transformations. You can refer to textbooks, online resources, or consult your teacher or classmates for additional guidance.