Question

Find the domain and range of the exponential function h(x)= -343^x

Answer 1

I will named this exponential function as y= - 343^x .
This function is symmetrical with function y = 343^x in relation to X axis. 
In general their formula is y=a^x or in your case y= - a^x

First I'll describe y=a^x => this function has domein Dx=R ( Whole field of real number), range is in interval ( 0,  +infinity), when x increases and y increases, when x decreases and y decreases. This function is always positive in whole domain and always is growing function. And X axis is its asymptote (y=0).

In your case function y= - 343^x has folowing features:
domein Dx=R
range is in interval (-infinity, 0)
when x increases => y decreases =>
example: y= -2^2=-4, y= -2^3=-8 etc....
when x decreases => y increases ->
example: y= -2^(-2)= - 1/(2^2)= - 1/4, y=-2^(-3)= - 1/(2^3)= - 1/8 etc....
this function is always negative
this function is always declining
x axis is its asymptote from the top ( y=0)