$g(x) = 8(3)^x - 6$\nselect all the transformations of $g(x)$ if the parent function is $f(x)=3^x$.\n1…

$g(x) = 8(3)^x - 6$\nselect all the transformations of $g(x)$ if the parent function is $f(x)=3^x$.\n1. vertical translation down 6 units\n2. reflection\n3. horizontal translation left 6 units\n4. vertical translation up 6 units\n5. vertical stretch

$g(x) = 8(3)^x - 6$\nselect all the transformations of $g(x)$ if the parent function is $f(x)=3^x$.\n1. vertical translation down 6 units\n2. reflection\n3. horizontal translation left 6 units\n4. vertical translation up 6 units\n5. vertical stretch

Answer

Answer:

  1. vertical translation down 6 units
  2. vertical stretch

Explanation:

Step1: Identify vertical stretch factor

For $g(x)=a(b)^x + k$ with parent $f(x)=b^x$, $a=8>1$ means vertical stretch by factor 8.

Step2: Identify vertical translation

$k=-6$ means vertical translation down 6 units.

Step3: Eliminate incorrect options

No reflection sign, no horizontal shift term, so other options are invalid.