Transformations of Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

f(x) = a| x - h | + k, where (h, k) is the vertex and 'a' determines the direction and width.

Front

What does the 'a' value in the absolute value function affect?

Back

'a' affects the vertical stretch/compression and direction of the graph. If 'a' is negative, the graph opens downwards.

Front

How do you identify the vertex of the function f(x) = a| x - h | + k?

Back

The vertex is the point (h, k) on the graph.

Front

What is the effect of adding a constant outside the absolute value, like in f(x) = |x| + k?

Back

It translates the graph vertically. If k > 0, it moves up; if k < 0, it moves down.

Front

What is the effect of adding a constant inside the absolute value, like in f(x) = |x + h|?

Back

It translates the graph horizontally. If h > 0, it moves left; if h < 0, it moves right.

Front

What does the equation y = -|x| represent?

Back

It represents a reflection of the basic absolute value function across the x-axis.

Front

How do you determine the horizontal translation of the function f(x) = |x + 4| - 9?

Back

The graph shifts left by 4 units due to the '+4' inside the absolute value.

Front

What does the equation f(x) = |x| - 4 indicate about the graph?

Back

It indicates a vertical translation downwards by 4 units.

Front

What is the equation of the graph that opens downwards and has a vertex at (2, 4)?

Back

y = -|x - 2| + 4.

Front

How do you find the y-intercept of the function f(x) = |x - 3| + 5?

Back

Set x = 0: f(0) = |0 - 3| + 5 = 3 + 5 = 8. The y-intercept is (0, 8).