Question

Which function represents transforming f(x)=3^x with a reflection over the x-axis and a vertical shift of 4 units? 3^x+ 4, -3^x+ 4, 3^x-4, -3^x+4

Answer 1

the -3 reflects over the x axis  and + 4 gives vertical shift of 4 units  
Its option D.

Answer 2

Answer: $-3^x +4$

Step-by-step explanation:

The equation for the vertical reflection of a function f(x) across the x-axis is given by :-

$y=-f(x)$

The vertical shift of 'k'  units of a function g(x) is given by :-

 $y=g(x)+k$

Now, the equation for the vertical reflection of a function $f(x)=3^x$ across the x-axis is given by :-

$-f(x)=-3^x$

Then , the equation for the vertical shift of 4 units of function $-3^x$ is given by :-

$y=-3^x +4$

Hence, the function represents transforming $f(x)=3^x$ with a reflection over the x-axis and a vertical shift of 4 units

$y=-3^x +4$