Front

What is an absolute value function?

Back

An absolute value function is a function that describes the distance of a number from zero on the number line, denoted as f(x) = |x|.

Front

How does a reflection across the x-axis affect the graph of a function?

Back

A reflection across the x-axis inverts the graph of the function, changing all positive y-values to negative and vice versa.

Front

What does a horizontal shift of a function mean?

Back

A horizontal shift moves the graph of the function left or right along the x-axis. For example, f(x - h) shifts the graph right by h units.

Front

What is a vertical shift in a function?

Back

A vertical shift moves the graph of the function up or down along the y-axis. For example, f(x) + k shifts the graph up by k units.

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph taller.

Front

How do you write an absolute value function with a vertical stretch of 2?

Back

The function can be written as f(x) = 2|x|.

Front

What does the expression |x - 3| represent in terms of graph transformation?

Back

The expression |x - 3| represents a horizontal shift of the graph of |x| to the right by 3 units.

Front

How do you determine the value of a function at a specific point, such as f(-2)?

Back

To find f(-2), substitute -2 into the function and simplify to find the output value.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where a, b, c, and d affect the graph's shape and position.

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 graph (upward or downward).