Question

Given that ƒ(x) = 3^x, identify the function g(x) shown in the figure.Question 3 options:A) g(x) = −(1∕3)^xB) g(x) = −3^–xC) g(x) = −3^xD) g(x) = 3^−x

Answer 1

D)g(x) = 3^−x

Explanation

given the function

$f(x)=3^x$

it has a transformatio functio g(x), by checking the graph we can conclude the transformation was a reflection across y-xis

so, we need to apply the rule for that kind of transformation

the rule to reflect a function across the y-axis is

(x,y)→(−x,y)

$(x,y)\Rightarrow(-x,y)$

therfore, we need to negate the x coordiante, hence

$f(x)=3^x\Rightarrow reflection\text{ acrros y axis}\Rightarrow g(x)=3^{-x}$

therefore, the answer is

D)g(x) = 3^−x

I hope this helps you