Algebra 1: Topic 5-Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

What does the domain of a function represent?

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the average rate of change of a function?

Back

The average rate of change of a function over an interval is calculated by taking the difference in the function's values at the endpoints of the interval and dividing by the difference in the x-values.

Front

What is the vertex of an absolute value function in the form y = a|x - h| + k?

Back

The vertex of the function is the point (h, k), which represents the minimum or maximum point of the graph.

Front

What does the symbol |x| represent?

Back

The symbol |x| represents the absolute value of x, which is the distance of x from 0 on the number line, always non-negative.

Front

What is the effect of the coefficient 'a' in the function y = a|x - h| + k?

Back

The coefficient 'a' affects the vertical stretch or compression and the direction of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

How do you determine the domain of an absolute value function?

Back

The domain of an absolute value function is always all real numbers, represented as (-∞, ∞).

Front

What is the significance of the point (3, 1) in the function y = 2|x - 3| + 1?

Back

The point (3, 1) is the vertex of the function, indicating the minimum value of the function occurs at x = 3.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.