Unit 3A Review - Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input. It is defined as \( f(x) = |x| \), where \( |x| \) represents the absolute value of \( x \).

Front

What does the vertex of an absolute value function represent?

Back

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

Front

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

Back

A vertical stretch by a factor of \( k \) (where \( k > 1 \)) makes the graph narrower, while a vertical shrink (where \( 0 < k < 1 \)) makes it wider.

Front

What is the effect of a horizontal shift on the graph of an absolute value function?

Back

A horizontal shift moves the graph left or right. For example, \( f(x) = |x - 3| \) shifts the graph 3 units to the right.

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 and \( a \) determines the direction and width 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 graph. If \( a > 0 \), the graph opens upwards; if \( a < 0 \), it opens downwards.

Front

How do you determine if the vertex of an absolute value function is a minimum or maximum?

Back

If the function opens upwards (\( a > 0 \)), the vertex is a minimum. If it opens downwards (\( a < 0 \)), the vertex is a maximum.

Front

What is the inequality representation of an absolute value function?

Back

The inequality representation of an absolute value function can be written as \( f(x) \leq |x + 4| - 1 \) or \( f(x) \geq |x + 4| - 1 \), depending on the context.

Front

How do you find the vertex of the function \( f(x) = |x + 2| - 3 \)?

Back

The vertex can be found by identifying the values of \( h \) and \( k \) in the general form. Here, the vertex is at \( (-2, -3) \).

Front

What is the significance of the absolute value in the function \( f(x) = |x - 2| \)?

Back

The absolute value ensures that the output of the function is always non-negative, representing the distance from the point 2 on the x-axis.