Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

View step-by-step help

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=f(t)=17000-3100t

. Find the domain and range of

f(t)

.

Identify Function Components: Identify the function and its components. $\newline$ Function: $V = f(t) = 17000 - 3100t$ $\newline$ This equation shows how the value $V$ of a car decreases over time $t$ .
Determine Domain of $f(t)$ : Determine the domain of $f(t)$ . The domain of $f(t)$ is all possible values of $t$ for which the function is defined. Since $t$ represents the age of the car in years, $t$ must be a non-negative number ( $t \geq 0$ ).
Calculate Zero Value Time: Calculate when the car's value reaches zero 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 a fraction of a year old in this context, round $t$ down to the nearest whole number, $t = 5$ .
State Domain Limit: State the domain based on the calculation. $\newline$ The domain of $f(t)$ is $0 \leq t \leq 5$ , as the car's value cannot be negative and the car is valued for up to $5$ years.
Determine Range of f(t): Determine the range of $f(t)$ . The range of $f(t)$ is the set of all possible values of $V$ . From $t = 0$ to $t = 5$ , the value of $V$ decreases from $17000$ to $0$ .
State Range Values: State the range based on the function's behavior. $\newline$ The range of $f(t)$ is from $0$ to $17000$ , as these are the maximum and minimum values $V$ can take.

More problems from Write and solve direct variation equations

Question

Write an expression to represent:

\newline

3

more than the product of

2

x

Posted 3 months ago

Question

Write an expression to represent:

4

times the difference of

x

2

Posted 3 months ago

Question

Write an expression to represent:

4

less than the product of

1

x

Posted 3 months ago

Question

What happens to the value of the expression

35+k

k

\newline

1

\newline

(A) It increases.

\newline

(B) It decreases.

\newline

(C) It stays the same.

Posted 3 months ago

Question

h(x)=x^{-5}

\newline

h^{\prime}(2)=

Posted 3 months ago

Question

\mathrm{D}=\left[\begin{array}{ll}4 & -1 \\ 2 & -1\end{array}\right]

A=\left[\begin{array}{rrr} 3 & 1 & 0 \\ 2 & 1 & -2 \end{array}\right]

\newline

\mathrm{H}=\mathrm{DA}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

B=\left[\begin{array}{rr} 4 & 4 \\ 1 & 0 \\ -2 & 1 \end{array}\right] \text { and } F=\left[\begin{array}{ll} 0 & 3 \\ 0 & 1 \end{array}\right]

\newline

\mathrm{H}=\mathrm{BF}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

F=\left[\begin{array}{rr}2 & 3 \\ 0 & 5 \\ -1 & -1\end{array}\right]

\mathrm{D}=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]

\newline

\mathrm{H}=\mathrm{FD}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 5 \\ 5 & 5 & 0\end{array}\right]

F=\left[\begin{array}{rr}-2 & -1 \\ 5 & 2 \\ 5 & -2\end{array}\right]

\newline

\mathrm{H}=\mathrm{EF}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

\mathrm{C}=\left[\begin{array}{r} -1 \\ -2 \\ 2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 2 & 1 \end{array}\right]

\newline

\mathrm{H}=\mathrm{CD}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago