Question

30 POINTS PLS HELP

Answer 1

Answer:

We proceed to use the following operations: (i) Vertical translation downwards ($k = -\frac{1}{2}$), (ii) Vertical compression ($c = \frac{1}{2}$), (iii) Vertical translation upwards ($k = \frac{1}{2}$). The graph is presented below.

Step-by-step explanation:

To transform $y = \frac{5}{4}\cdot x + \frac{1}{2}$ into $y = \frac{5}{8}\cdot x + \frac{1}{2}$, we apply the following steps:

(i) Vertical translation downwards ($k = -\frac{1}{2}$)

$g(x) = f(x) +k$ (1)

(ii) Vertical compression ($c = \frac{1}{2}$)

$g(x) = c\cdot f(x)$ (2)

(iii) Vertical translation upwards ($k = \frac{1}{2}$)

$g(x) = f(x) + k$

Now, we proceed to transform the primitive expression:

Step 1

$f'(x) = \frac{5}{4}\cdot x$

Step 2

$f''(x) = \frac{5}{8}\cdot x$

Step 3

$g(x) = \frac{5}{8}\cdot x + \frac{1}{2}$

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.