Final Answer:
The function should be graphed as f(x) = 2x² - 3, with a domain of all real numbers and a range of y ≥ -3. This function is related to the graph of the parent function y = x², but it has been vertically stretched by a factor of 2 and shifted downward by 3 units.
Step-by-step explanation:
The function f(x) = 2x² - 3 can be graphed by first recognizing that it is a quadratic function in the form f(x) = ax^2 + c, where a is the coefficient of x^2 and c is the constant term. In this case, a = 2 and c = -3. The graph of this function will be a parabola opening upwards, with its vertex at the point (0, -3). The domain of this function is all real numbers, as there are no restrictions on the input values of x. The range can be determined by analyzing the vertex of the parabola, which gives us y ≥ -3.
This function is related to the graph of the parent function y = x² through its transformation. The parent function y = x² represents a basic parabola with its vertex at the origin. The function f(x) = 2x² - 3 is obtained from y = x² by vertically stretching it by a factor of 2, causing it to become narrower, and shifting it downward by 3 units. These transformations result in a parabola that opens upwards, has a vertex at (0, -3), and is narrower than the parent function.
In summary, the graph of f(x) = 2x² - 3 is a vertically stretched and downward-shifted version of the parent function y = x². Its domain includes all real numbers, and its range consists of all y-values greater than or equal to -3.