Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

Consider the function $f\left(x\right)=\frac{x}{x+4}$.

(a) Is the point $\left(1,\frac{1}{4}\right)$ on the graph of function.

(b) if $x=-2$, what is $f\left(x\right)$. What point is on the graph of f ?

(c) If $f\left(x\right)=2$, what is x? What point is on the graph of f ? 

Step-by-Step Solution

Answer

Part (a). The point $\left(1,\frac{1}{4}\right)$is not on the graph of the function.

Part (b). $f\left(x\right)=-1$, point $\left(-2,-1\right)$ is on the graph.

Part (c) .$x=-8$, point $\left(-8,2\right)$ is on the graph.

Step 1. Given information.

The given function is $f\left(x\right)=\frac{x}{x+4}$.

Part (a) Step 1. Check the point 1 , 1 4 on the graph of the function.

Put the coordinates of the points $\left(x,y\right)=\left(1,\frac{1}{4}\right)$ in the equation.

$$\begin{gathered} f\left(x\right)=\frac{x}{x+4} \\ \frac{1}{4}=\frac{1}{1+4} \\ \frac{1}{4}\ne \frac{1}{5} \end{gathered}$$

The point is not satisfy the equation, so the point is not on the graph of the function.

Part (b) Step 1. Find the value of f ( x )   when   x = - 2 .

The given function is $f\left(x\right)=\frac{x}{x+4}$.

Put $x=-2$ into the function.

$$\begin{gathered} f\left(x\right)=\frac{x}{x+4} \\ f(-2)=\frac{-2}{-2+4} \\ f(-2)=\frac{-2}{2}=-1 \end{gathered}$$

So, when $x=-2$ the value of the function is $-1$.

The point on the graph of f is $\left(-2,-1\right)$.

Part (c) Step 1. Find the value of x when f ( x ) = 2 .

The given function is $f\left(x\right)=\frac{x}{x+4}$.

Put $f\left(x\right)=2$ into the function.

$$\begin{gathered} f\left(x\right)=\frac{x}{x+4} \\ 2=\frac{x}{x+4} \\ 2x+8=x \\ 2x-x+8=0 \\ x+8=0 \\ x=-8 \end{gathered}$$

So, the when $f\left(x\right)=2$, the value of $x=-8$.

The point on the graph of f is $\left(-8,2\right)$.