Question

What is the graph of the function f(x) = the quantity of x squared plus 3 x minus 4, all over x plus 4?

Answer 1

Given the function:

f(x) = the quantity of x squared plus 3x minus 4 , all over x plus 4

i,e

`f(x) = (x^2+3x-4)/(x+4)`

or

`f(x) = (x^2+4x-x-4)/(x+4)`

or

`f(x) = (x(x+4)-1(x+4))/(x+4)`

or

`f(x) = ((x+4)(x-1))/(x+4)`

⇒y= f(x) = x -1 ......[1]

Find the x-intercepts and y-intercepts for the equation [1] ;

y-intercepts defined as the graph crosses the y-axis;

substitute x =0 to solve for y;

y = 0-1 = -1

y = -1

x-intercepts defined as the graph crosses the x-axis;

substitute y =0 to solve for x;

0 = x-1

or

x = 1

Plot these points (0 , -1) and (1, 0) on the graph for the given function as shown below.