key features of graphs 1

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function has a range of $$0 \leq y < \infty$$ , it means the function can output any value starting from 0 to positive infinity.

A decreasing interval is a section of the graph where the function's output values decrease as the input values increase. For example, if a function is decreasing on the interval $$-\infty < x \leq 2$$ , it means that as x approaches 2 from the left, the function's values are getting smaller.

If a function has no decreasing interval, it means that the function is either increasing or constant throughout its domain. For example, if a function is always increasing or flat, it does not have any intervals where it decreases.

The y-intercept of a graph is the point where the graph crosses the y-axis. It can be found by setting x = 0 in the function's equation. For example, if the y-intercept is (0, -3), it means the graph crosses the y-axis at -3.

The domain of a function is the set of all possible input values (x-values) that the function can accept. For example, if the domain is $$1 \leq x < \infty$$ , it means the function can accept any value starting from 1 to positive infinity.

The y-intercept is significant because it provides information about the function's value when the input is zero. It can help in understanding the function's behavior and position on the graph.

To determine the range of a function from its graph, observe the lowest and highest points on the graph. The range is the set of y-values that the graph covers.

A function is increasing if, as the input values (x) increase, the output values (y) also increase. This can be identified on a graph where the slope is positive.

An open interval does not include its endpoints, while a closed interval includes its endpoints. For example, $$(a, b)$$ is open, and $$[a, b]$$ is closed.

The x-intercept of a graph is the point where the graph crosses the x-axis. It can be found by setting y = 0 in the function's equation.