Question

Bob is analyzing two linear functions, f(x) and g(x). Will they intersect? f(x) graph of the function f of x equals 2x + 3 g(x) x g(x) −2 4 −1 1 0 −2

Answer 1

The first function is given by equation
`f(x)=2x+3.`

The second function is given by the table

`\begin{array}{cccc}x&-2&-1&0\\f(x)&4&1&-2\end{array}`

To write the rule of g(x) you have to substitute two points into the equation

`g(x)=ax+b.`

1) When x=-2, g(x)=4 and 4=-2a+b;

2)When x=-1, g(x)=1 and 1=-a+b.

Subtract from the second equation the first equation:

1-4=-a+b-(-2a+b),

-3=-a+b+2a-b,

-3=a.

If a=-3, then b=1+a=1-3=-2 and the equation of g(x) is g(x)=-3x-2.

The slopes of f(x) and g(x) are 2 and -3 respectively.

Since these numbers are different, the lines will not be parallel, thus, they will intersect.