Let
t--------> the time in hours
d-------> the distance in miles
we know that
[tex]d=16t[/tex]
this is a linear equation that represent the scenario
in this equation the independent variable is the time t and the dependent variable is the distance d
The distance's equation in function notation is equal to
[tex]f(t)=16t[/tex]
Using a graph tool
see the attached figure
The domain of the function is the interval----------> [0,∞)
[tex]t\geq0[/tex]
The range of the function is the interval-------> [0,∞)
[tex]f(t)\geq0[/tex]
Statements
a) The independent variable, the input, is the variable d, representing distance
The statement is false
Because the independent variable is the variable t
b) The distance traveled depends on the amount of time Marlene rides her bike
The statement is true
Because the distance's equation in function notation is equal to
[tex]f(t)=16t[/tex]
c) The initial value of the scenario is 16 miles per hour
The statement is false
Because [tex]16[/tex] represent the rate or the slope of the linear equation
d) The equation t = d + 16 represents the scenario
The statement is false
Because, the scenario is represented by the function [tex]f(t)=16t[/tex]
e) The function f(t) = 16t represents the scenario
The statement is true
