Answer:
To graph the given piecewise function f(x), we will divide the x-axis into three intervals based on the given conditions: x ≤ -1, -1 < x < 4, and x ≥ 4.
For x ≤ -1:
In this interval, the function f(x) is defined as (3x - 5). To graph this portion of the function, we will substitute different x-values to find corresponding y-values and plot the points.
For example:
When x = -2, f(x) = (3(-2) - 5) = (-6 - 5) = -11.
When x = -1, f(x) = (3(-1) - 5) = (-3 - 5) = -8.
We can plot these points on the graph and connect them with a straight line.
- - -
For -1 < x < 4:
In this interval, the function f(x) is defined as (-2x + 3). Similarly, we will substitute different x-values to find corresponding y-values and plot the points.
For example:
When x = 0, f(x) = (-2(0) + 3) = (0 + 3) = 3.
When x = 3, f(x) = (-2(3) + 3) = (-6 + 3) = -3.
Again, we plot these points and connect them with a line segment.
- - -
For x ≥ 4:
In this interval, the function f(x) is defined as 2. This means that for any value of x greater than or equal to 4, f(x) will be equal to 2.
We plot a horizontal line at y = 2 for all x-values greater than or equal to 4.
- - -
To summarize:
- For x ≤ -1, the graph will be a line with a negative slope passing through the points (-2, -11) and (-1, -8).
- For -1 < x < 4, the graph will be a line segment with a negative slope passing through the points (0, 3) and (3, -3).
- For x ≥ 4, the graph will be a horizontal line at y = 2.
By connecting these three parts of the graph, we can visualize the piecewise function f(x) accurately.
Explanation:
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