HW Absolute Value Functions

Front

What is the axis of symmetry for an absolute value function?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves. For the function given in the quiz, the axis of symmetry is x = 15.

Front

What is the vertex of an absolute value function?

Back

The vertex is the highest or lowest point on the graph of an absolute value function, depending on whether it opens upwards or downwards.

Front

How do you write an absolute value function given transformations?

Back

To write an absolute value function, apply the transformations to the parent function y = |x|. For example, a reflection across the x-axis, a vertical shift right 2 units, and a horizontal shift down 7 units results in y = -|x - 2| - 7.

Front

What is the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of an absolute value function that opens downwards?

Back

The range of a downward-opening absolute value function is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What does it mean for a function to reflect across the x-axis?

Back

Reflecting across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical shift in the context of graph transformations?

Back

A vertical shift moves the graph up or down without changing its shape. A positive shift moves it up, while a negative shift moves it down.

Front

What is a horizontal shift in the context of graph transformations?

Back

A horizontal shift moves the graph left or right. A positive shift moves it to the right, while a negative shift moves it to the left.

Front

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

Back

The vertex can be found from the equation in the form y = a|x - h| + k, where (h, k) is the vertex.

Front

What is the effect of the coefficient 'a' in the absolute value function y = a|x - h| + k?

Back

The coefficient '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 negative, it opens downwards.