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30 POINTS PLS HELP
The slope of the linear function y= 5/4x +1/2 is changed to 5/8 where y= 5/8x + 1/2. Identify the transformation required to produce the new slope, state the equation of the transformed function, ande explainw hat the graph of the tranfsformed line look like.
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30 POINTS PLS HELP The Slope Of The Linear Function Y 54x 12 Is Changed To 58 Where Y 58x 12 Identify The Transformation Required To Produce The New Slope State class=

Sagot :

xero099

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.

View image xero099
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