60.6k views
0 votes
Which function represents g(x), a reflection of f(x) = On a coordinate plane, 2 exponential functions are shown. g (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1) and crosses the y - axis at (0, 0.5).(3)x across the y-axis? g(x) = 2(3)x g(x) = −One-half(3)x g(x) = One-half(3)−x g(x) = 2(3)−x

User Pjam
by
8.0k points

2 Answers

4 votes

Answer:

g(x)=1/2(3^-x)

User Wek
by
8.4k points
1 vote

Answer:


g(x)=(1)/(2)(3^(-x))

Explanation:

Given:

The graph of function
f(x)\ and\ g(x) are given.

The equation for
f(x) is given as:


f(x)=3^x

Now, the graph of
g(x) is a reflection of
f(x).

The graph of
g(x) passes through the point (-1, 1.5) [second quadrant] and crosses the y-axis at (0, 0.5).

As evident from the graph, the functions
f(x)\ and\ g(x) are reflections about the y-axis.

We know the transformation rule for reflection about the y-axis as:


f(x)\to f(-x)\\\\\therefore 3^x\to3^(-x)....(\textrm{Reflection about y-axis})

Now, the y-intercept of the function
y=3^(-x) is obtained by plugging in
x=0. This gives,


y=3^0=1

So, the y-intercept is at (0, 1). But the graph of
g(x) crosses the y-axis at (0, 0.5). As we observe, the coordinate rule for the transformation can be written as:

(0, 1) → (0, 0.5)


(x,y)\to (x,(1)/(2)y)

So, the reflected graph is compressed vertically by a factor of
(1)/(2).

Therefore, the transformation is given as:


y\to (1)/(2)y\\\\\therefore 3^(-x)\to (1)/(2)(3^(-x))

Therefore, the equation for
g(x) is:


g(x)=(1)/(2)(3^(-x))

User George Bora
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories