Question

Graph the function f(x) = x^2 for the domain (-2, 2). The graph of g is obtained from the graph of f with a transformation 3 units down. How are the equations, domains, and ranges of f and g related?

What is the graphed function f(x) = x^2 for the given domain (-2, 2)?
a) A parabola opening upwards.
b) A linear function.
c) A sine wave.
d) A constant function.

Answer 1

The graph of f(x) = x^2 for the domain (-2, 2) is a parabola opening upwards. The transformation 3 units down results in g(x) = x^2 - 3 with the same domain but a range that is shifted downward by 3 units.

Step-by-step explanation:

The graph of the function f(x) = x^2 for the domain (-2, 2) is a parabola opening upwards. This function demonstrates a quadratic relationship, where each value of x within the domain corresponds to a unique value of y (x^2), resulting in a curved graph. The transformation applied to function f to create function g, which is moving it 3 units down, would result in the function g(x) = x^2 - 3. The domain of g remains the same as f, which is (-2, 2). However, the range of g would be affected by the downward shift, decreasing all y-values of f by 3 units.