6.2k views
2 votes
Graph the step function over the interval -2 ≤ x ≤ 2 f(x) = [x + 3]

User Quasiyoke
by
8.3k points

1 Answer

6 votes

Graph of the Step Function f(x) = [x + 3] over -2 ≤ x ≤ 2

Here's how to graph the step function f(x) = [x + 3] over the interval -2 ≤ x ≤ 2:

1. Identify the Step Levels:

The step function f(x) = [x + 3] takes different integer values depending on the input x. Within the given interval:

For x < -2, f(x) = [x + 3] = -2 (since any number less than -2 added to 3 will still be less than 2).

For -2 ≤ x ≤ -1, f(x) = [x + 3] = 2 (rounding -1 + 3 up to the nearest integer gives 2).

For x > -1, f(x) = [x + 3] = 3 (since any number greater than -1 added to 3 will be greater than 2).

2. Draw Horizontal Lines:

Draw a horizontal line at y = -2 for all x values between -2 and -1.

Draw a horizontal line at y = 2 for all x values between -1 and 0.

Draw a horizontal line at y = 3 for all x values between 0 and 2 (including 2).

3. Connect the Lines with Vertical Jumps:

At x = -1, draw a vertical jump from the line at y = -2 to the line at y = 2. This represents the sudden change in the function's value from -2 to 2 as x crosses -1.

At x = 0, draw another vertical jump from the line at y = 2 to the line at y = 3. This represents the change in value from 2 to 3 as x crosses 0.

4. Label the Axes:

Label the x-axis as "x."

Label the y-axis as "f(x)."

5. (Optional) Show Discontinuities:

If needed, you can mark the points -1 and 0 with small open circles to signify the discontinuities where the function jumps between different levels.

This will give you the complete graph of the step function f(x) = [x + 3] over the interval -2 ≤ x ≤ 2. Remember that step functions have distinct jumps at integer values where the function's output changes abruptly.

Graph the step function over the interval -2 ≤ x ≤ 2 f(x) = [x + 3]-example-1
User Andrew Radulescu
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories