Answers:
The number 0 goes in the first blank for f(x)
The number 6 goes in the second blank for g(x)
----------------------------------------------------------------------------------
Explanation:
As x gets larger and larger, the expression (4/5)^x will get smaller and smaller. What's going on is that we are repeatedly multiplying (4/5) with itself over and over if we assume x is some whole number. For example, if x = 100, then we'll have 100 copies of (4/5) multiplied out. Each time we multiply by (4/5), the result gets smaller.
The results will approach 0 but not actually get there. So this is why f(x) has the horizontal asymptote y = 0. The function values f(x) will essentially be the set of positive y values, in other words, y > 0. This covers the range for f(x). To get the range of g(x), we add 6 to the range of f(x). This is because everything on g(x) is a vertical shift upward of 6 units.
Answer:
Step-by-step explanation:
This limit can be written as follows
Direct substitution means that we substitute in the value for x to get our limit
A translation
(I'm assuming that this isn't multiple choice since you didn't include the answer choices.)
Answer:
2/ 10^12
Step-by-step explanation:
see image below:)
Answer:
3x:4x for some real number x
Step-by-step explanation:
Since answer choices weren't provided, I generalized my answer.
First, notice we can simplify 6:4 into 3:2 because we can write the ratio as a fraction and simplify (6 and 4 are both multiples of 2).
Since 3 and 2 are relatively prime and the ratio cannot simplify anymore, we can say that the ratio of 6:4 = 3:2 = 3x:2x for some real number x because we can see that 3x:2x = 3:2 by simplifying (3x and 3 are both multiples of x).
As long as the answer choice you choose matches the format above, you should be correct! I hope this helps! :)
