The average gas mileage m in miles per gallon for a compact car is modeled by m(s)= -0.015(s - 47)^2 + 33, where s is the car’s speed in miles per hour.
The average gas mileage for an SUV is modeled by my(s)= -0.015(s - 47)^2 + 15.
What kind of transformation describes this change and what does this transformation mean?
We have been given that average gas mileage m in miles per gallon for a compact car is modeled by m(s) = - 0.015(s - 47)2 +33 and mileage for an SUV is modeled by my(s) = -0.015(s - 47)2 + 15.
We can see that both functions are parabolic and opens downwards. The vertex of function m(s) is (47,33), while vertex of function my(s) is (47,15). We can describe this change by translation.
This transformation means that function m(s) is translated 18 units downwards and average mileage of SUV is 18 miles/hour lesser than compact car at equal speeds.
The transformation that describes the change in gas mileage is a translation or shift, specifically a vertical shift.
In both models, the common term "-0.015(s - 47)^2" represents a quadratic function with a vertex at (47, 0).
For the compact car model, the term "+ 33" means the entire graph is shifted vertically 33 units upward, which means the graph is moved above the x-axis. This transformation represents that the average gas mileage for the compact car is higher than that for the SUV.
For the SUV model, the term "+ 15" means the entire graph is shifted vertically 15 units upward, which means the graph is also moved above the x-axis. This transformation represents that the average gas mileage for the SUV is lower than that for the compact car.
The function m(s) represents the average gas mileage for a compact car, while the function my(s) represents the average gas mileage for an SUV. Both functions have similar forms, -0.015(s - 47)^2 + C, with C being a constant. The transformation that describes this change is a translation or shift of the graph of the function m(s) to obtain the graph of the function my(s).
In particular, the transformation involves shifting the graph of m(s) downward by 18 units to obtain my(s). This can be seen by comparing the constant term in both functions: 33 for m(s) and 15 for my(s). The constant term represents the gas mileage when the car's speed is the same (47 miles per hour), so the shift represents a decrease in gas mileage for the SUV compared to the compact car.
Therefore, the transformation can be described as a vertical shift downward by 18 units, meaning that the average gas mileage for the SUV is 18 miles per gallon lower than that of the compact car at the same speed.