Question

If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

Answer 1

Answer:

Given the functions: $f(x)= -x^2 +3x+5$ and $g(x) = x^2+2x$

Now, calculate first $(f+g)(x)$ ;

$(f+g)(x) = f(x) + g(x)$

Substitute the given values we have;

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

Combine like terms;

$(f+g)(x) =5x+5$

Let y = $(f+g)(x)$

Then, we have y = 5x+5

Now, Graph the equation of the line y =5x +5

Using slope intercept form: An equation of line is given by :

y = mx +b ; where m is the slope of the line and b is the y-intercept.

On comparing we get;

m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)

Now, find the intercepts of the equation: y=5x+5;

x-intercepts: The graph or line crosses the x-axis i.,e

Substitute y = 0 and solve for x;

0 = 5x +5

Subtract 5 on both sides we get;

-5 = 5x

Divide both sides by 5 we get;

x = -1

x-intercepts= = (-1, 0)

Similarly for y-intercept:

Substitute the value of x= 0 and solve for y;

y = 5(0)+5

y = 5

y-intercepts = (0, 5)

Now, using these point we can draw a graph of function $(f+g)(x) =5x+5$ as shown below in the attachment.

Answer 2

f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x

(f + g)(x) = –x2 + 3x + 5 + x2 + 2x 
(f + g)(x) =   5x + 5