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

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

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Ratio and Quadratic equation

Full solution

Q.

\newline

The price value,

V

, of a car that is

t

years old is given by

V=f(t)=17000-3100 t

. Find thr domain and range of

f(t)

.

Identify Function Components: Identify the function and its components. $\newline$ $V = f(t) = 17000 - 3100t$
Determine Domain of $f(t)$ : Determine the domain of $f(t)$ . The domain of $f(t)$ is all values of $t$ for which the function makes sense. Since $t$ represents time in years, $t$ must be non-negative ( $t \geq 0$ ).
Calculate Zero Value Point: Calculate when the car value becomes zero or negative. $\newline$ Set $V = 0$ for boundary of domain. $\newline$ $0 = 17000 - 3100t$ $\newline$ $3100t = 17000$ $\newline$ $t = \frac{17000}{3100}$ $\newline$ $t = 5.48$
Interpret Domain Result: Interpret the result for domain. The car's value cannot be negative, so the maximum value for $t$ is when $V$ reaches zero, approximately at $t = 5.48$ years. Thus, the domain is $[0, 5.48]$ .
Determine Range of $f(t)$ : Determine the range of $f(t)$ . The range is the set of all possible values of $V$ . From $t = 0$ to $t = 5.48$ , $V$ decreases from $17000$ to $0$ .

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