do the following for the function given below. (speed, stopping distance of a car) a. describe an…
do the following for the function given below. (speed, stopping distance of a car) a. describe an appropriate domain and range for the function. b. make a rough sketch of a graph of the function. c. briefly discuss the validity of the graph as a model of the true function. c. briefly discuss the validity of the graph as a model of the true function. choose the correct answer below. a. the validity of the graph as a model of the true function can never be known. b. the graph is a valid model of the function because it is reasonable to assume that speed in miles per hour increases as stopping distance in feet increases. c. the graph is not a valid model of the true function. d. the graph is a valid model of the function because it is reasonable to assume that stopping distance in feet increases as speed in miles per hour increases.
Answer
Explanation:
Step1: Analyze domain and range
The speed of a car cannot be negative in this context, so the domain (speed) is $x\geq0$. The stopping - distance also cannot be negative, so the range (stopping distance) is $y\geq0$.
Step2: Sketch the graph
As speed ($x$) increases, the stopping distance ($y$) increases. The graph starts at the origin $(0,0)$ and is a curve that goes upwards and to the right.
Step3: Evaluate graph validity
In real - life, as the speed of a car increases, the stopping distance also increases. So the graph is a valid model of the function.
Answer:
a. Domain: $x\geq0$ (where $x$ is speed in miles per hour), Range: $y\geq0$ (where $y$ is stopping distance in feet) b. A curve starting at the origin $(0,0)$ and increasing upwards and to the right. c. D. The graph is a valid model of the function because it is reasonable to assume that stopping distance in feet increases as speed in miles per hour increases.