The domain is what values we can have for x. We don't have any fractions or square roots, so there's nothing that x can't be.
Answer: The domain is (0,+Infinity)
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The range is what values we can have for y.
Look at 8^x. x can be large and positive (8^x will be large and positive), x can be small and positive (8^x will be positive, greater than 1, but very close to 1), x can be large and negative (8^x will be positive, but very close to 0), and x can be small and negative (8^x will be positive, less than 1, but very close to 1). If x is 0, then 8^x is 1.
8^x can be anything positive. That means -1.7 * (8^x) can be anything negative. Y can be anything negative.
The range is (-Infinity,0)
Here's the graph plotted on Google: https://www.google.com/?gws_rd=ssl#safe=on&q=plot+-1.7*8%5Ex
Note: The graph looks like it drops off around x = 8, but x doesn't stop. The reason it looks like that is because -1.7*8^x becomes a very very negative number very fast. For example, at x = 10, y = about -1.8 billion, which is hard to graph. Around x = 110, y = -1 googol.