For Exercises 1-6, refer to the basic graphs in A-F A.(IMAGE...

For Exercises $1-6,$ refer to the basic graphs in $A-F$
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Which is the graph of $f(x)=x^{2} ?$ Give the domain and range.

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Key Concepts

Range

The range of a function is the set of all possible output values it can produce. For f(x) = x², the outputs are always non-negative because the square of any real number is non-negative. Therefore, the range is all real numbers greater than or equal to zero, typically expressed as [0, ?).

Domain

The domain of a function represents all possible input values for which the function is defined. Since any real number can be squared in f(x) = x², the domain is all real numbers, from negative infinity to positive infinity.

Parabola

The graph of a quadratic function is a parabola. For f(x) = x², this parabola opens upward, is symmetric about the y-axis, and has its vertex at the origin. The parabolic shape illustrates how the function's values increase as the absolute value of x increases.

Quadratic Function

A quadratic function is a second-degree polynomial, typically expressed as f(x) = ax² + bx + c. In the case of f(x) = x², the function takes a simple form where the output is the square of the input, resulting in a specific and symmetric parabolic shape.

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