Questions on piecewise function graphing
Obviously I can't get help with the actual graphing here but I am hoping someone can push me in the right direction
Problem: f(x) {4, if 0<=x<2}
{5, if 2<=x<4}
{6, if 4<=x<6}
So how would I get started?
What does the 4,5 and 6 mean?
For example for the first equation x is greater than or equal to zero and less than two. So that that mean two of my points on a graph will have something to do with 0 and 1?
I know its a lot of questions but I am just hoping someone will push me in the right direction :)
This function looks like a flight of stairs.
Between 0 and 2, y is 4
Between 2 and 4, y is 5
Between 4 and 6, y is 6
Ok, make your graph paper. For 0<x<2, y is 4. Draw the y=4 line from x=0 to x<2
Then, from 2<=x to <4, y is 5. Draw the line y=5 from x=2 to x<4
then y= 6 for the next step.
To get started with graphing the given piecewise function, you will need to plot points on a coordinate plane based on the different ranges of x-values and their corresponding function values.
Let's break it down step by step:
1. Start by drawing a set of axes on a piece of graph paper or using a graphing tool on your computer.
2. Remember that the function f(x) has different rules (or cases) depending on the value of x. In your case, there are three distinct cases for different ranges of x-values.
3. The numbers 4, 5, and 6 represent the function values of f(x) for the given ranges of x-values. In other words, when x falls within the range 0 ≤ x < 2, the function value is 4. When x is between 2 ≤ x < 4, the function value is 5, and for 4 ≤ x < 6, the function value is 6.
4. Now, let's start plotting points on the graph. For the first case, when 0 ≤ x < 2, the function value is 4. This means that any x-value between 0 and 2 (excluding 2) should have a corresponding y-value of 4. So you can plot points like (0, 4) and (1, 4) on your graph.
5. For the second case, when 2 ≤ x < 4, the function value is 5. This means that any x-value between 2 and 4 (excluding 4) should have a corresponding y-value of 5. So you can plot points like (2, 5) and (3, 5) on your graph.
6. Similarly, for the third case, when 4 ≤ x < 6, the function value is 6. This means that any x-value between 4 and 6 (excluding 6) should have a corresponding y-value of 6. So you can plot points like (4, 6) and (5, 6) on your graph.
7. Finally, connect the plotted points with line segments to visualize the function graph. Since the function values remain constant within each range, you will have horizontal line segments connecting the points within each case.
By following these steps, you should be able to graph the given piecewise function f(x).