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The price value,
V, of a car that is
t years old is given by
V=J(t)=17000-3100 t. Find the domain and range of
f(t).

The price value, $V$ , of a car that is $t$ years old is given by $V=J(t)=17000-3100 t$ . Find the domain and range of $f(t)$ .

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Write and solve direct variation equations

Full solution

Q. The price value,

V

, of a car that is

t

years old is given by

V=J(t)=17000-3100 t

. Find the domain and range of

f(t)

.

Identify Domain: Identify the domain of the function $V=J(t)=17000-3100t$ . Since $t$ represents the age of the car in years, $t$ must be a non-negative number. Therefore, the domain is all non-negative real numbers, or $t \geq 0$ .
Find Upper Limit: Determine when the car value becomes zero or negative to find the upper limit of the domain. $\newline$ Set $V=0$ and solve for $t$ : $\newline$ $0 = 17000 - 3100t$ , $\newline$ $3100t = 17000$ , $\newline$ $t = \frac{17000}{3100}$ , $\newline$ $t = 5.48$ . $\newline$ Since a car can't be partially a year old in this context, we consider $t$ up to $5$ years.

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