Answer:
We proceed to use the following operations: (i) Vertical translation downwards ([tex]k = -\frac{1}{2}[/tex]), (ii) Vertical compression ([tex]c = \frac{1}{2}[/tex]), (iii) Vertical translation upwards ([tex]k = \frac{1}{2}[/tex]). The graph is presented below.
Step-by-step explanation:
To transform [tex]y = \frac{5}{4}\cdot x + \frac{1}{2}[/tex] into [tex]y = \frac{5}{8}\cdot x + \frac{1}{2}[/tex], we apply the following steps:
(i) Vertical translation downwards ([tex]k = -\frac{1}{2}[/tex])
[tex]g(x) = f(x) +k[/tex] (1)
(ii) Vertical compression ([tex]c = \frac{1}{2}[/tex])
[tex]g(x) = c\cdot f(x)[/tex] (2)
(iii) Vertical translation upwards ([tex]k = \frac{1}{2}[/tex])
[tex]g(x) = f(x) + k[/tex]
Now, we proceed to transform the primitive expression:
Step 1
[tex]f'(x) = \frac{5}{4}\cdot x[/tex]
Step 2
[tex]f''(x) = \frac{5}{8}\cdot x[/tex]
Step 3
[tex]g(x) = \frac{5}{8}\cdot x + \frac{1}{2}[/tex]
The graph of both function are now presented below. The parent function is the red line and the new function is represented by the blue line.
