Transformations of Functions Flashcard

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable or expression, representing the distance from a certain value on the number line.

Front

How do you solve the absolute value inequality |x - a| < b?

Back

To solve |x - a| < b, you split it into two inequalities: a - b < x < a + b.

Front

What does the inequality |L - 12| ≤ 0.3 represent in the context of manufacturing?

Back

It represents that the acceptable lengths of the rulers can vary from 11.7 inches to 12.3 inches, ensuring they are within a tolerance of 0.3 inches from the target length of 12 inches.

Front

What is the vertex of the function y = |x - 5| - 3?

Back

The vertex is the point (5, -3), which is the minimum point of the graph.

Front

How does the graph of y = |x| differ from y = |x - 5|?

Back

The graph of y = |x| is centered at the origin (0,0), while y = |x - 5| is shifted 5 units to the right.

Front

What is the effect of the negative sign in front of the absolute value in y = -|x|?

Back

The negative sign reflects the graph of y = |x| across the x-axis, creating a downward-opening V shape.

Front

What does the expression |x + 1| < 3 represent graphically?

Back

It represents the interval where x is between -4 and 2, shown as an open interval (-4, 2) on the number line.

Front

How do you graph the function y = |x| - 2?

Back

Start with the graph of y = |x|, then shift it down by 2 units.

Front

What is the solution set for the inequality |x - 1| > 3?

Back

The solution set is x < -2 or x > 4, representing values outside the interval (-2, 4).

Front

What is the significance of the 'tolerance' in manufacturing?

Back

Tolerance defines the acceptable range of variation in a manufactured product, ensuring it meets quality standards.