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vivado [14]
3 years ago
10

Consider f(x) = 2x2 + 1 and g(x) = 3x − 6. Which statement about f + g is true?

Mathematics
1 answer:
disa [49]3 years ago
7 0

Given:

The two functions are:

f(x)=2x^2+1

g(x)=3x-6

To find:

The correct statement about the function f+g.

Solution:

We have,

f(x)=2x^2+1

g(x)=3x-6

Adding both functions, we get

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

f+g=2x^2+1+3x-6

f+g=2x^2+3x-5

It is a quadratic function. So, option A is incorrect and option B is correct.

The domain of f+g is all real numbers because it is defined for all real values of x. So, option C is incorrect.

The range of f+g cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.

Therefore, the correct option is B.

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3 years ago
What is the equation of the function that is graphed as line a?
valentinak56 [21]
F(x)=-1x-1

1)  Pick 2 points on the line (i chose (-4,3) and (3,-4)
2) Find slope of the line using the 2 points. (work below)
3) Find y-intercept, which is the point where y-axis and the line cross (y-intercept is -1).
4) Place both slope and y-intercept into slope-intercept form, y=mx+b (m=slope and b=y-intercept.)
5) Change y to f(x) (meaning function of x).

Work:
3-(-4)/-4-3=3+4/-4-3=7/-7=-1

y-intercept equals -1 also.

y=mx+b
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