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 of the graph.

Front

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

Back

'h' represents the horizontal shift of the graph. If h is positive, the graph shifts right; if negative, it shifts left.

Front

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

Back

'k' represents the vertical shift of the graph. If k is positive, the graph shifts up; if negative, it shifts down.

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

'a' affects the vertical stretch or compression and the direction of the graph. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

What is the effect of a negative 'a' in the function f(x) = -|x|?

Back

The graph reflects over the x-axis, creating a downward-opening V shape.

Front

What is the vertex of the function f(x) = |x + 3| - 2?

Back

The vertex is (-3, -2).

Front

What is the transformation of the function f(x) = |x| when it becomes f(x) = |x - 4| + 1?

Back

The graph shifts right 4 units and up 1 unit.

Front

If f(x) = |x| + 3, what is the y-intercept of the graph?

Back

The y-intercept is (0, 3).

Front

What is the equation of the absolute value function that opens downwards with vertex (2, 5)?

Back

f(x) = -|x - 2| + 5.

Front

How do you determine the x-intercepts of the function f(x) = |x - 1| - 3?

Back

Set f(x) = 0: |x - 1| - 3 = 0, which gives x = 4 and x = -2.