Question

• graph the function. the horizontal values represent the input, and the vertical values represent the output.

for function ( f ), the values of ( f(x) ) are the vertical values, which are often labeled ( y ), so we can write ( y = f(x) ). because ( f(x) ) is defined by the expression ( 5(x + 2) ), we can graph ( y = 5(x + 2) ).
for function ( m ), we can write ( y = m(x) ) and graph ( y = 3 - \frac{1}{2}x ).
two graphs are shown here, one for ( y = f(x) ) and one for ( y = m(x) ) on coordinate grids

• find the input when we know the output.

suppose the output of function ( f ) is 65 at some value of ( x ), or ( f(x) = 65 ), and we want to find out what that value is. because ( f(x) ) is equal to ( 5(x + 2) ), we can write ( 5(x + 2) = 65 ) and solve for ( x )
\begin{align}5(x + 2) &= 65 \\x + 2 &= 13 \\x &= 11end{align}
each function here is a linear function because the value of the function changes by a constant rate and its graph is a line.

Explanation:

Step1: Start with the equation

We have the equation \( 5(x + 2)=65 \). Our goal is to solve for \( x \).

Step2: Divide both sides by 5

To isolate the term with \( x \), we divide both sides of the equation by 5.
\( \frac{5(x + 2)}{5}=\frac{65}{5} \)
Simplifying both sides, we get \( x + 2 = 13 \).

Step3: Subtract 2 from both sides

Now, to solve for \( x \), we subtract 2 from both sides of the equation \( x + 2 = 13 \).
\( x + 2 - 2 = 13 - 2 \)
Simplifying, we find \( x = 11 \).

Answer:

The value of \( x \) is \( \boldsymbol{11} \).