For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
<h3>
How to work with vertical and horizontal shifts?</h3>
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
- If N > 0, the shift is upwards.
- If N < 0, the shift is downwards.
For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
- If N > 0, the shift is to the left.
- If N < 0, the shift is to the right.
Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
Learn more about translations
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Answer:
Specific Learning Outcomes:
Solve problems that involve finding powers of a number
Description of mathematics:
In this problem students work with powers of numbers and, as a consequence, come to understand what is happening to the numbers.
Students also see how an apparently enormous and difficult calculation can be broken down into manageable parts. The students should come to realise that there are only a limited number of unit digits obtained when 7 is raised to a power. Further, these specific digits 'cycle round' as the power of 7 increases. This cycle is 7, 9, 3, 1, 7, 9, …
The same is true of the digit in the tens place.
Answer:
Graph 1 is not proportional
Graph 2 is proportional - y is 2 times x
Step-by-step explanation:
In graph 1, there is no x-y correlation
In graph 2, there is, when x=1, y=6
when x=2, y=12. Therefore, when x=3 y would equal 18.
