Answer:
radius = 5 in
Step-by-step explanation:
Using the formula for calculating the area (A) of a circle
A = πr² ( r is the radius )
here A = 78.5, hence
3.14r² = 78.5 ( divide both sides by 3.14 )
r² = = 25 ( take the square root of both sides )
r = = 5
The two graphs are represented below.
Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.
There are 3 ways to change a function:
Now, the points for f(x) are:
(-5,0) (0,6) (5,-4) (8,0)
And the points for g(x) are:
(-5,-3) (0,-9) (5,1) (8,-3)
Comparing points:
(-5,0) → (-5,-3)
(0,6) → (0,-9)
(5,-4) → (5,1)
(8,0) → (8,-3)
It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:
(-5,0-3) → (-5,-3)
(0,6-15) → (0,-9)
(5,-4+5) → (5,1)
(8,0-3) → (8,-3)
Then, the vertical change is a <u>Vertical</u> <u>Shift</u>.
Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a <u>Reflection</u>.
<u>Range</u> <u>of</u> <u>a</u> <u>function</u> is all the values y can assume after substituting the x-values.
<u>Domain</u> <u>of</u> <u>a</u> <u>function</u> is all the values x can assume.
Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.
Any vertical translation will change the range of a function and keep domain intact.
Then, for f(x) and g(x):
graph translation domain range
f(x) none [-5,8] [-4,6]
g(x) vertical shift [-5,8] [-9,1]
<u>In conclusion, this transformation (or translation) will affect the range of g(x)</u>
