Answer:
Step-by-step explanation:
It was given that, florida manatee population is 3,000 and is decreasing by 11% each year.
We want to write a function for this situation.
Since the population is decreasing annually, it is modelled by:
We substitute the give initial population and rate of decrease to get:
This simplifies to:
Answer:
52.8 feets
Step-by-step explanation:
From the diagram :
The height of tree woulb be :
Height above the ground (at breakpoint) + hypotenus
Hypotenus, h cab be obtained using Pythagoras rule :
h² = opp² + adj²
h² = 39² + 12²
h² = 1665
h = sqrt(1665)
h = 40.804 feets
Height of tree to the nearest tenth ;
40.804 feets + 12 feets
= 52.804 feets
= 52.8 feets
The attached picture is a summary of all the six transformations you'd do.
Any change outside the f(x) notation impacts y-values of points on the graph.
Any changes inside the f(x) notation impacts x-values of points on the graph.
The trick is that the inside changes are usually the opposite of what you'd expect to have happen.
7. y=f(x)+8
This is an outside change. You're adding 8 to all the y-values of points on the graph. This will shift your entire graph up 8 units.
8. y=f(x+6)
This is an inside change. Because it says "+6", you want to think, "Ah! That means I'll actually subtract 6 from the x-value of every point on the graph." This graph is shifted 6 units to the left.
9. y=-f(x)
Inside change, impacts y-values. Every y-value will be given the opposite signs. Negatives become positive and positives become negative. This will flip your graph over the x-axis.
10. y = f(-x) + 5
Give this one a shot on your own first in a comment and I'll let you know how you did.
11. y = - 3 f(x-3)
There are three things happening. A negative on the outside, multiplying by 3 on the outside, and subtracting 3 inside. What will each of those do individually? Take a shot on this one and let me know what you think.
12. y = 1/2 f( 1/2 x )
Again, three changes. Try this one and let me know what you think. Remember multiplying by 1/2 inside really means you'll do the opposite of multiplying by 1/2.
