Question

Find the domain and range of the exponential function h(x) = –343 x . Explain your findings. As x decreases, does h increase or decrease? Explain. As x increases, does h increase or decrease? Explain.

Answer 1

Domain = { x : x ∈ R } ( set of all real numbers )

Range = { y ∈ R : y < 0 } ( all negative real numbers )

Explanation:

Given exponential function,

`h(x)=-343^x`

∵ Domain ( possible values of input ) of an exponential function is the set of all real numbers,

So, the Domain of the given function h(x) is R (set of all real numbers),

Now,

`f(x) = -343^x\implies f(x) = -1(343)^x`

So, for any value of x ( even or odd )

h(x) will always give the negative values,

Hence, h(x) < 0

i.e. the range of h(x) = { y ∈ R : y < 0 }