This is a piecewise function on one graph:
f(x)= 3, -4 <or= x <or= 1
-x+2, 1 < x < 3
x-5, 3 <or= x <or= 7
The coordinates are (-4,3) (-1,3) (3,-1) (3,-2) (7,2)
So what would the graph look like if it is:y= abs(f(x)), y=2f(abs(x)), y=f(-x), y=-f(x)-3, y=f(x+3), y=f(2x). You can put down the coordinate or if u have another way of showing me, please do. Thank you.
To graph the given piecewise function, y = f(x), it is important to understand the function values for different ranges of x.
For -4 ≤ x ≤ 1, the function is constant and equal to 3. So, you can represent this segment of the function as a horizontal line at y = 3.
For 1 < x < 3, the function is -x + 2. This represents a downward-sloping line segment passing through the points (1, 1) and (3, -1).
For 3 ≤ x ≤ 7, the function is x - 5. This represents an upward-sloping line segment passing through the points (3, -2) and (7, 2).
To graph the different composite functions, let's go through them one by one:
1) y = |f(x)|:
To graph this, take the original graph of f(x) and ensure that any negative values are reflected above the x-axis. Since f(x) is always positive or zero, the graph of y = |f(x)| will be identical to the original graph.
2) y = 2f(|x|):
To graph this, multiply the function values found in the original graph by 2. Additionally, reflect any negative x-values across the y-axis to ensure that the absolute value remains positive.
3) y = f(-x):
To graph this, take the original graph and reflect it across the y-axis. The x-values become their negatives, but the y-values remain the same.
4) y = -f(x) - 3:
To graph this, take the original graph and reflect it across the x-axis. In addition, slide the graph 3 units downward (subtracting 3 from all y-values).
5) y = f(x + 3):
To graph this, take the original graph and shift it horizontally by 3 units to the left. All x-values will be decreased by 3 units.
6) y = f(2x):
To graph this, take the original graph and compress it horizontally by a factor of 2. All x-values will be multiplied by 1/2.
By applying these transformations to the original graph, you can obtain the graphs for the given composite functions.