Question

Which two functions could be combined by addition to
result in the function shown in the graph?
f(x) = 5x² and g(x) = x +1
f(x) = 2x and g(x) = 5x
f(x) = 2x + 3 and g(x) = x + 1
f(x) = 2x2 and g(x) = 5x + 3

Answer 1

The two functions that when added can represent the given graph is the pair in the last option, which gives:

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

Which two functions could be combined to get the graph?

We can see that the y-intercept of the graph of the parabola is at y = 3, then we need to see two options that have constants such that their sum is equal to 3.

This is because when we evaluate in x = 0, the function takes the value of the constant. For example in a quadratic:

y = a*x^2  + b*x + c

The y-intercept is c.

There is only one option that meets this condition, and this is the last option:

f(x) = 2x^2 and g(x) = 5x + 3

When we add these we get:

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

If you want to learn more about parabolas, you can read:

https://brainly.com/question/1480401