A2U1 Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, represented as f(x) = |x|.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

How does the graph of y = |x + 2| + 2 move compared to y = |x|?

Back

The graph of y = |x + 2| + 2 moves left 2 units and up 2 units compared to y = |x|.

Front

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

Back

The vertex of the function f(x) = |x - 3| + 1 is (3, 1).

Front

How do you translate the graph of f(x) = |x - 2| + 1 four units down and three units left?

Back

The new equation after translating is f(x) = |x + 1| - 3.

Front

What is the slope of the absolute value function y = 2|x - 4| - 6?

Back

The slope of the function y = 2|x - 4| - 6 is 2, meaning it rises 2 units for every 1 unit it moves to the right.

Front

What does it mean for an absolute value function to open upwards?

Back

An absolute value function opens upwards when the coefficient of the absolute value expression is positive.

Front

What is the effect of a negative coefficient in front of an absolute value function?

Back

A negative coefficient in front of an absolute value function causes the graph to open downwards.

Front

How do you find the vertex of an absolute value function in the form f(x) = a|x - h| + k?

Back

The vertex is located at the point (h, k).

Front

What is the transformation of the function f(x) = |x| when it is written as f(x) = |x - 4| + 3?

Back

The function f(x) = |x - 4| + 3 is translated right 4 units and up 3 units from the parent function f(x) = |x|.