Algebra Unit 7 Lesson 1 Practice

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the non-negative value of x. The graph of an absolute value function has a V shape.

Front

What does the vertex of an absolute value function represent?

Back

The vertex of an absolute value function represents the minimum or maximum point of the graph, depending on the orientation. It is the point where the graph changes direction.

Front

How does the graph of y = |x - 3| differ from y = |x|?

Back

The graph of y = |x - 3| is shifted 3 units to the right compared to y = |x|. The vertex of y = |x - 3| is at (3, 0).

Front

What effect does the coefficient in front of the absolute value have?

Back

The coefficient affects the steepness of the graph. For example, in f(x) = a|x|, if |a| > 1, the graph is steeper; if 0 < |a| < 1, the graph is wider.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx - h| + k, where (h, k) is the vertex, 'a' affects the direction and steepness, and 'b' affects the horizontal stretch.

Front

What does it mean for a graph to never cross the x-axis?

Back

A graph that never crosses the x-axis indicates that the function has no real roots. For example, the function f(x) = |x| + 1 is always above the x-axis.

Front

How do you determine the vertex of the function f(x) = |x + 4| - 3?

Back

The vertex of f(x) = |x + 4| - 3 is at the point (-4, -3). This is found by setting the expression inside the absolute value to zero.

Front

What is the transformation represented by f(x) = |x| - 7?

Back

The transformation represented by f(x) = |x| - 7 is a vertical shift downward by 7 units from the basic graph of y = |x|.

Front

What is the significance of the 'h' value in the function f(x) = a|bx - h| + k?

Back

The 'h' value in the function represents a horizontal shift. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the term 'domain' refer to in the context of functions?

Back

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