Transformations of Absolute Value Functions

Front

What is the equation of the absolute value parent function?

Back

y = |x|

Front

What does it mean to vertically compress a function by a factor of 1/4?

Back

The function's output values are multiplied by 1/4, making it 'flatter'.

Front

What is the effect of reflecting a function over the y-axis?

Back

The function's graph is mirrored across the y-axis, changing the sign of the x-values.

Front

What does it mean to translate a function up by 3 units?

Back

Every point on the graph of the function is moved 3 units higher on the y-axis.

Front

What is the transformation represented by g(x) = -|1/2(x+3)|-1?

Back

Reflection over the x-axis, horizontal stretch by a factor of 2, translation left 3 units and down 1 unit.

Front

How do you identify the transformations of f(x) = 1/3 |x + 4| - 2?

Back

Horizontal translation left 4 units, vertical shrink by a factor of 3, vertical translation down 2 units.

Front

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

Back

It reflects the graph over the x-axis.

Front

What does a vertical stretch by a factor of 3 do to a function?

Back

It multiplies the output values by 3, making the graph steeper.

Front

How do you determine the vertex of an absolute value function?

Back

The vertex is found at the point where the expression inside the absolute value equals zero.

Front

What is the general form of a transformed absolute value function?

Back

y = a|bx - h| + k, where (h, k) is the vertex.