Absolute value functions and graphs

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, denoted as f(x) = |x|.

Front

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

Back

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

Front

What does the transformation 'vertical shrink by a factor of 3' mean for the function f(x) = 1/3 |x|?

Back

It means that the output values of the function are reduced to one-third of their original values, making the graph wider.

Front

How does a horizontal translation to the left affect the graph of f(x) = |x|?

Back

A horizontal translation to the left shifts the graph of f(x) = |x| to the left by the specified number of units.

Front

What is the effect of a vertical translation down 2 units on the function f(x) = |x|?

Back

It shifts the entire graph of f(x) = |x| down by 2 units, moving the vertex from (0,0) to (0,-2).

Front

What is the parent function of absolute value?

Back

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

Front

What does the notation f(x) = a|x - h| + k represent?

Back

This notation represents a transformed absolute value function where 'a' affects the vertical stretch/shrink, 'h' affects horizontal translation, and 'k' affects vertical translation.

Front

What is the interval where the function f(x) = |x - 3| is decreasing?

Back

The function f(x) = |x - 3| is decreasing on the interval (-inf, 3).

Front

If f(x) = 2|x|, what type of transformation is applied to the parent function?

Back

The function is vertically stretched by a factor of 2.

Front

What is the value of K in the function f(x) = 4|x + 2| - 3?

Back

K is -3, which represents a vertical translation down 3 units.