Respuesta :

meerkat18
Given:

f(x) = (x2 + 5x + 6)/(x+3)

Required:

type of graph

Solution:

The function given can be simplified further. By factoring x2 + 5x + 6, we get (x+3)(x+2). Dividing it by (x+3), we are left with f(x) = x+2.

Therefore, the plot is a linear plot with a positive slope of 1 and a y-intercept of 2.

Answer:

We have to graph the function f(x) which is represented as:

[tex]f(x)=\dfrac{x^2+5x+6}{x+3}[/tex]

We can write the function f(x) as:

[tex]f(x)=\dfrac{x^2+3x+2x+6}{x+3}\\\\f(x)=\dfrac{x(x+3)+2(x+3)}{x+3}\\\\f(x)=\dfrac{(x+3)(x+2)}{x+3}\\\\f(x)=x+2[/tex]

i.e. we get the equation of function f(x) as a linear function with x-intercept at (-2,0) and y-intercept at (0,2).

so, the graph of function f(x) is a straight line passing through (0,2) and (-2,0).

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