Breaking Down the Function f(x) = |x – 3| – 1: Step-by-step Explanation and Graph

f(x) = |x – 3| – 1

To better understand the function f(x) = |x – 3| – 1, let’s break it down step by step:

1

To better understand the function f(x) = |x – 3| – 1, let’s break it down step by step:

1. Absolute Value: The absolute value of a number is always positive and represents the distance of that number from zero on a number line. As indicated by the vertical bars surrounding the expression (x – 3), this means we’ll be working with the distance between x and 3.

2. Difference: The expression (x – 3) represents the difference between x and 3. If x is greater than 3, the expression evaluates to a positive value. If x is less than 3, the expression evaluates to a negative value.

3. Absolute Value of (x – 3): The absolute value of (x – 3) ensures that the result is always positive, regardless of whether (x – 3) is positive or negative.

4. Subtract 1: Finally, subtracting 1 from the absolute value of (x – 3) shifts the entire graph down by 1 unit.

Now, let’s look at the graph of f(x) = |x – 3| – 1:

1. Graph the basic linear function y = x: This is a straight line with a slope of 1 and passing through the origin.

2. Apply the absolute value: For x > 3, the graph remains the same. However, for x < 3, the graph reflects or "flips" over the x-axis. 3. Shift the graph down by 1: Move the entire graph downward by 1 unit. Combining these steps, we obtain the graph of f(x) = |x - 3| - 1.

More Answers: