Characteristics of Graphs

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

The parent function of a quadratic function is $$f(x) = x^2$$ .

The transformation represents a shift left by 3 units and down by 1 unit.

A vertical stretch by a factor of 2 means that the output values (y-values) of the function are multiplied by 2.

The negative interval is the range of x-values where the function outputs negative values.

The range of the function $$f(x) = x^2$$ is $$[0, \text{infinity})$$ .

A horizontal compression by a factor of 1/2 means that the input values (x-values) are halved, making the graph narrower.

Shifting a function up by 4 units means that every point on the graph of the function is moved 4 units higher.

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.

This notation indicates a logarithmic function with base 10.