Multiplying the input of a function by a positive constant number expands or compresses the function horizontally
Please find attached the required graph of the function [tex]y = f \left(\dfrac{1}{2} \cdot x \right)[/tex]
Method:
The horizontal expansion or compression of a function f(x) is given as follows;
Parent function; y = f(x)
Expanded or compressed function, y = f(k·x)
Where 0 < k < 1, the graph of the function is expanded
Where k > 1, the graph of the function is compressed
The image of the (x, y) in f(x) becomes (k·x, y) in the function f(k·x) of the
The points in the given function are;
(-4, 2), (-2, -2), and (0, 0)
The given graph has two parts
The equation of the first [part of the graph is y = -2·(x + 2) - 2
Which gives;
y = -2·x -6
The equation for [tex]y = f \left(\dfrac{1}{2} \cdot x \right)[/tex], is therefore;
[tex]y = f \left(\dfrac{1}{2} \cdot x \right) = -x - 6[/tex]
The equation for the second part of the graph is y = f(x) = x
Therefore;
[tex]y = f \left(\dfrac{1}{2} \cdot x \right) = \dfrac{1}{2} \cdot x[/tex]
The coordinates of the point where the y-values are equal is therefore;
0.5·x = -x - 6
1.5·x = -6
x = -4
Plotting the two equations from the origin to their common solution then to the point y = 2 gives;
First part; (0, 0), (-2, -1), (-4, -2)
Second part; (-4, -2), (-6, 0), (-8, 2)
With the above points, the graph of [tex]y = f \left(\dfrac{1}{2} \cdot x \right)[/tex], is plotted
Please find the required graph created with MS Excel
Learn more about graphs here:
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