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

Front

What does it mean for a graph to be vertically compressed by a factor of 2/5?

Back

It means that the y-values of the function are multiplied by 2/5, making the graph flatter compared to the original.

Front

How does shifting a graph up by 6 units affect its equation?

Back

The equation of the function is modified by adding 6 to the output, resulting in f(x) = |x| + 6.

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.

Front

What does the 'a' in the absolute value function's equation represent?

Back

The 'a' represents the vertical stretch or compression factor and determines the steepness of the graph.

Front

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

Back

A negative 'a' value reflects the graph across the x-axis.

Front

How do you translate the function f(x) = |x| down by 2 units?

Back

The translated function is f(x) = |x| - 2.

Front

What is the equation of the absolute value function that has a vertex at (0, 4)?

Back

The equation is f(x) = |x| + 4.

Front

How do you express the absolute value function that is shifted left by 4 units?

Back

The function is expressed as f(x) = |x + 4|.

Front

What is the equation of the absolute value function that is vertically stretched by a factor of 4?

Back

The equation is f(x) = 4|x|.