Question

Linear Functions Given Verbally A verbal description of a linear function$f$is given. Express the function$f$in the form$f\left(x\right)=ax+b$.

The linear function$g$has rate of change$-12$and initial value$100$.

Short answer

The required function is $g\left(x\right)=-12x+100$.

Step-by-step solution

Step 1. Definition of linear function.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as:

$f\left(x\right)=ax+b$ … (i)

Where$a$ is the rate of change and$b$ is the initial value, and both are real numbers.

Step 2. Given information.

The linear function$g$ has rate of change$-12$ and the initial value $100$.

Step 3. Write the function.

The range of change is $-12$, so $a=-12$. The initial value is $100$, so $b=100$.

Substitute$a=-12$ and$b=100$ in (i) to find the function $g$.

$\begin{array}{l}g\left(x\right)=\left(-12\right)x+\left(100\right)\\ g\left(x\right)=-12x+100\end{array}$

Thus, the required function is $g\left(x\right)=-12x+100$.