To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x²? What is its domain?

Verified step by step guidance

1. Identify the function given: \( f(x) = x^2 \). This is a quadratic function, which typically graphs as a parabola opening upwards.
2. Recall the basic shape of the graph of \( y = x^2 \): it is a U-shaped curve symmetric about the y-axis, with its vertex at the origin \( (0,0) \).
3. To determine which graph corresponds to \( f(x) = x^2 \), look for the graph that has this characteristic parabola shape opening upwards.
4. Next, consider the domain of \( f(x) = x^2 \). Since you can square any real number, the domain includes all real numbers.
5. Express the domain in interval notation as \( (-\infty, \infty) \), meaning the function is defined for every real value of \( x \).

Key Concepts

Graph of a Quadratic Function

A quadratic function like ƒ(x) = x² produces a parabola when graphed. This parabola opens upwards with its vertex at the origin (0,0). Recognizing this shape helps identify the correct graph among options.

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For ƒ(x) = x², any real number can be squared, so the domain is all real numbers, often written as (-∞, ∞).

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output value. Understanding how to evaluate ƒ(x) = x² for various x-values helps in plotting points and confirming the graph's shape.