Question

the graph of f(x) = 1/2 (2.5)x and its reflection across the x-axis, g(x), are shown. what is the range of g(x)? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0

Answer 1

D

Explanation:

Took the test

Answer 2

The correct option is 2. The range of g(x) is all real numbers less than 0.

Explanation:

The given function is

`f(x)=(1)/(2)(2.5)^x`

If a graph reflected across x axis, then

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

The function f(x) reflected across x-axis, so

`g(x)=-f(x)`

`g(x)=-(1)/(2)(2.5)^x`

It is an exponential function.

`g(x)\rightarrow -\infty\text{ as }x\rightarrow \infty`

`g(x)\rightarrow 0\text{ as }x\rightarrow -\infty`

Since the value of g(x) lies between
`-\infty` and 0, therefore the range of g(x) is all real numbers less than 0. Option 2 is correct.