Question

On a coordinate plane, 2 exponential fuctions are shown. Function f (x) decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 6) and goes through (1, 2). Function g (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 2) and crosses the y-axis at (0, 6).


Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?



g(x) = −6(one-third) Superscript x


g(x) = −6(one-third) Superscript negative x


g(x) = 6(3)x


g(x) = 6(3)−x

Answer 1

Answer:

$g(x)=6(3)^x$

Step-by-step explanation:

We are given  that

$f(x)=6(\frac{1}{3})^x$

Function f decreases from quadrant  2 to quadrant 1 and approaches  y=0

It cut the y- axis at (0,6) and passing through the point (1,2).

Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.

It passing through the point (-1,2) and cut the y-axis at point (0,6).

Reflection across y- axis:

Rule of transformation is given by

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

Using the rule then we get

$g(x)=6(\frac{1}{3})^{-x}=6(3)^x$

By using

$x^{-a}=\frac{1}{x^a}$

Substitute x=-1

$g(-1)=6\times (\frac{1}{3})=2$

Substitute x=0

$g(0)=6$

Therefore,$g(x)=6(3)^x$ is true.

Answer 2

Answer:

C) g(x) = 6(3)x