Test 10/30 - Transformation of Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative output.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph, 'a' determines the vertical stretch or compression and direction of the graph.

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards. The absolute value of 'a' affects the steepness of the graph.

Front

What is the vertex of the function f(x) = -3|x - 1| + 4?

Back

The vertex is at the point (1, 4).

Front

How do you find the y-intercept of an absolute value function?

Back

To find the y-intercept, set x = 0 in the function and solve for f(0).

Front

What is the y-intercept of f(x) = -|x - 1| + 4?

Back

The y-intercept is (0, 5).

Front

What does the transformation 'x - h' represent in the function f(x) = a|x - h| + k?

Back

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

Front

What does the transformation '+ k' represent in the function f(x) = a|x - h| + k?

Back

The transformation '+ k' represents a vertical shift of the graph upwards by 'k' units.

Front

What is the effect of the transformation 'x + 1' on the graph of f(x) = |x|?

Back

The transformation 'x + 1' shifts the graph of f(x) = |x| to the left by 1 unit.

Front

How do you determine if a function is decreasing or increasing?

Back

A function is increasing if its slope is positive and decreasing if its slope is negative over an interval.