Absolute Value & Piecewise Graphs

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How does the graph of y = |x| transform when we subtract a constant?

Back

The graph slides down by the value of the constant subtracted.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

What effect does adding a constant to the absolute value function have on its graph?

Back

Adding a constant to the function moves the graph up by that constant value.

Front

What does the expression |x - a| represent in terms of graph transformation?

Back

The expression |x - a| represents a horizontal shift of the graph to the right by 'a' units.

Front

If g(x) = |x + 2|, how does this graph compare to the parent function?

Back

The graph of g(x) = |x + 2| is shifted left by 2 units compared to the parent function.

Front

What is the maximum value of a piecewise function?

Back

The maximum value of a piecewise function is the highest output value among all defined pieces of the function.

Front

How do you determine the vertex of the graph of an absolute value function?

Back

The vertex of the graph of an absolute value function y = |x - h| + k is the point (h, k).

Front

What is the effect of a negative sign in front of the absolute value function, such as in y = -|x|?

Back

A negative sign in front of the absolute value function reflects the graph across the x-axis.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and ensure to indicate open or closed endpoints.