which of the following describes the transformations of g(x)=-(2)^(x + 4)-2 from the parent function…

which of the following describes the transformations of g(x)=-(2)^(x + 4)-2 from the parent function f(x)=2^x? shift 4 units left, reflect over the x - axis, shift 2 units down shift 4 units left, reflect over the y - axis, shift 2 units down shift 4 units right, reflect over the x - axis, shift 2 units down shift 4 units right, reflect over the y - axis, shift 2 units down

which of the following describes the transformations of g(x)=-(2)^(x + 4)-2 from the parent function f(x)=2^x? shift 4 units left, reflect over the x - axis, shift 2 units down shift 4 units left, reflect over the y - axis, shift 2 units down shift 4 units right, reflect over the x - axis, shift 2 units down shift 4 units right, reflect over the y - axis, shift 2 units down

Answer

Explanation:

Step1: Analyze horizontal shift

For a function $y = f(x + h)$, if $h>0$, it shifts $h$ units left. In $g(x)=-(2)^{x + 4}-2$, compared to $f(x)=2^{x}$, we have $h = 4$, so it shifts 4 units left.

Step2: Analyze reflection

The negative sign in front of $(2)^{x+4}$ in $g(x)=-(2)^{x + 4}-2$ reflects the function over the x - axis. For a function $y=-f(x)$, it is a reflection of $y = f(x)$ over the x - axis.

Step3: Analyze vertical shift

For a function $y=f(x)+k$, if $k<0$, it shifts $|k|$ units down. In $g(x)=-(2)^{x + 4}-2$, $k=-2$, so it shifts 2 units down.

Answer:

shift 4 units left, reflect over the x - axis, shift 2 units down