Find the translation and stretch from ##y=2^x## to ##y=2^{x+4}##

[chwala]

Homework Statement

See attached...

Relevant Equations

Translation/Stretch

For part (i) i was thinking of the vertical shift from $(0,1)$ to $(0,16)$, this can be given by;
$y=2^x + 15$ but it does not fit onto $y=2^{x+4}$ something wrong here.

For part (ii), =we have a stretch factor of $a=16>0$ (vertical stretch) thus, $y=16\cdot 2^x$

your thoughts...i do not have solutions...

 

[pasmith]

If $f(x) = 2^x$ then $2^{x+4} = f(x + 4)$.

 

[chwala]

If $f(x) = 2^x$ then $2^{x+4} = f(x + 4)$.

Isn't this a horizontal shift... it's not exactly what we want. Unless I am missing something...

 

[Mark44]

For part (i) i was thinking of the vertical shift from (0,1) to (0,16),

As already noted, the transformation is a horizontal translation (or shift). The original graph is translated four units to the left. The point on the original graph that was at (0, 1) is now at (-4, 1). The point that was at (4, 16) is now at (0, 16).

Isn't this a horizontal shift...

Yes.

 

[Mark44]

On the other hand, $2^{x + 4} = 2^x \cdot 2^4 = 16\cdot 2^2$.
Viewed this way there is a vertical stretch away from the x-axis.