3.15x4.12=
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The graph of g(x) obtained from the horizontal shrink, reflection and translation of f(x) by a factor of 16, across the x–axis and 2 units downwards is given by the function;
- g(x) = -(16•x)² - 2
Please see the attached graph of g(x)
<h3>What is a transformation of a function?</h3>The transformation of the graph of a function is the shrinking, stretching, reflecting or translating of the graph of the function
The given function is f(x) = x²
- The formula for reflecting a function f(x) across the x–axis to get g(x) is: g(x) = -f(x)
- The formula for shrinking of a function f(x) horizontally by a factor of 16 is g(x) = f(16•x)
- To translate the function, f(x), 2 units down gives; g(x) = f(x) - 2
The graph of g(x), which is a horizontal shrink by a factor of 16, a reflection across the x–axis and a vertical shift of 2 units downwards, is obtained from the function, g(x) = -f(16•x) - 2 = -(16•x)² - 2
Therefore;
- g(x) = -(16•x)² - 2
Please find attached the graph of g(x) created with Sheets
Learn more about the transformation of a function here:
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Remember that distance equals rate multiplied by time, or put more compactly, 
Here, we're looking for the distance traveled by a truck, given only its rate, 44 mph. We're also given that both of the vehicles travel for is the same. This lets us use the car's information to find that time, which we can then use to find the distance traveled by the truck.
For the car, our distance is 120 miles, our rate is 55 mph, and our time is unknown; let's call that value
. We have:
Dividing both sides by 55, we find:
So our time is 24/11 hours - roughly 2 hours and 13 minutes. We'll use the 24/11 value to get as exact an answer as we can, though.
For the truck, we know its rate and its time (24/11 hours), but we don't know its distance. We'll call it
. Putting in our new value for time, we have:
So, in 24/11 hours, the truck will have traveled 96 miles traveling at its average speed.
Here, we're looking for the distance traveled by a truck, given only its rate, 44 mph. We're also given that both of the vehicles travel for is the same. This lets us use the car's information to find that time, which we can then use to find the distance traveled by the truck.
For the car, our distance is 120 miles, our rate is 55 mph, and our time is unknown; let's call that value
Dividing both sides by 55, we find:
So our time is 24/11 hours - roughly 2 hours and 13 minutes. We'll use the 24/11 value to get as exact an answer as we can, though.
For the truck, we know its rate and its time (24/11 hours), but we don't know its distance. We'll call it
So, in 24/11 hours, the truck will have traveled 96 miles traveling at its average speed.