Which of the following statements are true about f (x) and g(x)? The graphs share the same axis of symmetry
The y -intercept for f() is greater than the y-intercept forg (+).
f(2) + g(4) = 0
f(-4) g(0)
The domain of f(x) has more elements than the domain of g(x).
The graphs share the same relative maximum.

We want to see which statements are true about the functions f(x) and g(x). The true statements are:

Let's read each statement and then let's see why is true or why is not true.

1) "The graphs share the same axis of symmetry"

We define the axis of symmetry as a vertical line that divides the graph in two halves, in the case of parabolas, the axis of symmetry always passes through the vertex.

So with this in mind,  you can clearly see that both functions have the same axis of symmetry, so this first statement is true.

2) "The y-intercept for f(x) is greater than the y-intercept for g(x)."

The y-intercept of a function is the value of y at which the graph intercepts the y-axis.

By looking at the graph, you can see that f(x) will intersect the y-axis way above than g(x), this implies that the statement is correct.

3) "f(2) + g(4) = 0"

By looking at the graph we can see that:

f(2) + g(4) = 2 + (-3) = -1

So the statement is false.

4) "The domain of f(x) has more elements than the domain of g(x)."

The domain is the set of values of x that the functions allow, because both are quadratic functions, both have the same domain, which is the set of all real numbers.

5) "The graphs share the same relative maximum."

Relative maximums are values of the function that are larger than the surrounding values in a given interval, here you can see that g(x) and f(x) don't have the same curvature (g(x) actually has a universal maximum) thus this is false.

If you want to learn more about quadratic functions, you can read: