12.9.24 PAP Transformations of Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph.

Front

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

Back

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

Front

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

Back

A positive 'a' value causes the graph to open upwards, creating a minimum point at the vertex.

Front

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

Back

A negative 'a' value causes the graph to open downwards, creating a maximum point at the vertex.

Front

What does the 'h' value in the absolute value function represent?

Back

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

Front

What does the 'k' value in the absolute value function represent?

Back

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

Front

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

Back

The vertex of the function is the point (h, k), which is the highest or lowest point of the graph depending on the value of 'a'.

Front

How do you write the equation of an absolute value function that is shifted right by 3 and down by 6?

Back

The equation would be g(x) = |x - 3| - 6.

Front

What transformation occurs when you replace f(x) with -f(x)?

Back

Replacing f(x) with -f(x) reflects the graph across the x-axis.

Front

What is the effect of a vertical compression by a factor of 1/5 on the graph of an absolute value function?

Back

A vertical compression by a factor of 1/5 makes the graph wider, reducing the steepness of the V-shape.