Respuesta :
Answer:
The original function would be [tex]g(x)=3|32x|+2[/tex]
Step-by-step explanation:
Recall the following transformation rules:
(i) vertically stretched by a factor of c ( c must be greater than 1):
f(x) is transformed to cf(x).
(ii) horizontally compressed by a factor of a ( a must be greater than 0):
f(x) is transformed to f(ax).
(iii) translated down a unit:
f(x) is transformed to f(x)-a
Consider the original function is g(x).
After vertically stretched by a factor of 2,
Transformed function is 2g(x).
After horizontally compressed by a factor of 1/4,
Transformed function is 2g(x/4).
Finally, translate down 6 units,
Transformed function is 2g(x/4) - 6.
According to the question,
[tex]2g(\frac{x}{4}) - 6 = f(x) = 6 |8x| -2[/tex]
[tex]2g(\frac{x}{4})-6=6 |8x| -2[/tex]
[tex]2g(\frac{x}{4})=6 |8x| -2+6[/tex]
[tex]2g(\frac{x}{4})=6 |8x| +4[/tex]
[tex]g(\frac{x}{4})=3 |8x| +2[/tex]
[tex]\implies g(y)=3 |32y| +2[/tex] ( Say x/4 = y )
Substitute x for y,
[tex]g(x) = 3 |32x| +2[/tex]
Hence, the original function would be [tex]g(x) = 3 |32x| +2[/tex] .
