translations of absolute value functions

Front

What does the absolute value function represent graphically?

Back

The absolute value function represents the distance of a number from zero on the number line, resulting in a V-shaped graph that opens upwards.

Front

How does the graph of f(x) = |x| + k translate vertically?

Back

The graph translates vertically by k units. If k is positive, it moves up; if k is negative, it moves down.

Front

What effect does adding a constant inside the absolute value function have on the graph?

Back

Adding a constant inside the absolute value function, f(x) = |x - h|, translates the graph horizontally. If h is positive, it moves right; if h is negative, it moves left.

Front

What is the vertex of the absolute value function f(x) = |x - h| + k?

Back

The vertex of the function f(x) = |x - h| + k is the point (h, k), which is the lowest point of the graph if it opens upwards.

Front

How do you determine if a graph of an absolute value function is narrow, wide, or the same as the parent function?

Back

The width of the graph is determined by the coefficient of the absolute value. If the coefficient is greater than 1, the graph is narrow; if it is between 0 and 1, it is wide; if it is 1, it is the same.

Front

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

Back

The range of the function f(x) = |x| is [0, infinity), meaning it includes all non-negative real numbers.

Front

What transformations occur in the function f(x) = |x + 3| - 5?

Back

The function translates left 3 units and down 5 units.

Front

What is the parent function of absolute value functions?

Back

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

Front

How does the graph of f(x) = -|x| transform compared to its parent function?

Back

The graph of f(x) = -|x| reflects the parent function across the x-axis, resulting in an upside-down V shape.

Front

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

Back

A negative sign in front of the absolute value function reflects the graph across the x-axis.