Parent Functions & Graph Characteristics Review

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (e.g., $$y = x$$ ), quadratic functions (e.g., $$y = x^2$$ ), and absolute value functions (e.g., $$y = |x|$$ ).

The x-intercept of a function is the point where the graph of the function crosses the x-axis. It is found by setting the output (y) to zero and solving for x.

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run). In the equation $$y = mx + b$$ , 'm' represents the slope.

The notation $$x \to -\text{∞}$$ indicates that the value of x is approaching negative infinity, meaning it is getting larger in the negative direction.

The general form of a quadratic function is $$y = ax^2 + bx + c$$ , where 'a', 'b', and 'c' are constants and 'a' is not equal to zero.

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. For the function $$y = ax^2 + bx + c$$ , the vertex can be found using the formula $$x = -\frac{b}{2a}$$ .

The absolute value function is defined as $$y = |x|$$ , which outputs the non-negative value of x. It creates a V-shaped graph.

A linear function can be identified by its straight-line graph. It has a constant slope and can be expressed in the form $$y = mx + b$$ .

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

An increasing function has a positive slope, meaning as x increases, y also increases. A decreasing function has a negative slope, meaning as x increases, y decreases.