Question

If f(x)= -x^2+3x+5 and g(x) =x^+2, which graph of (f+g)(x)

Answer 1

See explanation

Explanation:

If

`f(x)=-x^2 +3x+5`

and

`g(x)=x^2 +2,`

then

`(f+g)(x)=-x^2+3x+5+x^2+2=3x+7`

This is the linear function. To plot the graph of this function, find x- and y- intercepts:

x-intercept:

`y=0\Rightarrow 3x+7=0\\ \\3x=-7\\ \\x=-(7)/(3)`

y-intercept:

`x=0\Rightarrow y=3\cdot 0+7\\ \\y=7`

Plot these two points on the coordinate plane and connect them with a straight line.