1A.1 Absolute Value ETicket

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

What does the graph of the absolute value function f(x) = |x| look like?

Back

The graph is a V-shape that opens upwards, with the vertex at the origin (0,0).

Front

What is the minimum value of the absolute value function f(x) = |x|?

Back

The minimum value is 0, which occurs at x = 0.

Front

What is the domain of the absolute value function f(x) = |x|?

Back

The domain is all real numbers, denoted as (-∞, ∞).

Front

What is the range of the absolute value function f(x) = |x|?

Back

The range is all non-negative real numbers, denoted as [0, ∞).

Front

How does the graph of g(x) = |x - 2| differ from the parent function f(x) = |x|?

Back

The graph of g(x) = |x - 2| is the same V-shape as f(x) = |x| but is shifted 2 units to the right.

Front

What is the effect of adding a constant to the absolute value function, such as in f(x) = |x| + 2?

Back

Adding a constant shifts the graph vertically. For f(x) = |x| + 2, the graph shifts up by 2 units.

Front

What is the effect of multiplying the absolute value function by a negative number, such as in f(x) = -|x|?

Back

Multiplying by a negative number reflects the graph across the x-axis. The vertex remains at (0,0) but opens downwards.

Front

What is the range of the function f(x) = -|x| + 4?

Back

The range is all values less than or equal to 4, denoted as (-∞, 4].

Front

What is the domain of the function g(x) = |x + 3|?

Back

The domain is all real numbers, denoted as (-∞, ∞).