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Answer:
Parent function f(x) = x with f(x)+5 means the parent function will vertically shift 5 units up.
Step-by-step explanation:
<u>Vertical translation of f(x) is of the form</u>
It means if the constant 'k' is added in the output, the parent graph vertically shifted 'k' units up.
Given
Replacing the parent function f(x) = x with f(x)+5 means the parent function will vertically shift 5 units up.
Please also check the attached diagram.
-
The red graph shows the parent function i.e.
- The blue graph shows the transformed function i.e. f(x)+5
The blue graph is the result of the vertically shifting of the parent function by 5 units up.
Hence, parent function f(x) = x with f(x)+5 means the parent function will vertically shift 5 units up.
Using the information given and linear function concepts, it is found that:
- a) The equation is:
.
- b) The skydiver’s altitude after the parachute has been open for 2 minutes is of 2000 feet.
- c) It takes 200 seconds for the skydiver to reach the ground.
A linear function is modeled by:
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when t changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
Item a:
- The skydiver descends at a rate of 25 feet per second, hence
.
Then:
<u>90 seconds after the parachute opens, his altitude is 2750 feet</u>, which means that when , which is used to find b. Then:
Hence, the equation is:
.
Item b:
Time is in seconds, hence, this is y(120).
The skydiver’s altitude after the parachute has been open for 2 minutes is of 2000 feet.
Item c:
The time it takes to reach the ground is t for which y(t) = 0, hence:
It takes 200 seconds for the skydiver to reach the ground.
You can learn more about linear functions at brainly.com/question/26065573