Why don't you sketch the graph?
Which of the following functions, with domain D f = ( − ∞ , ∞ ) will have a graph which is a n-shaped parabola (it has a maximum point) with no y -intercept?
Details: It may or may not have x -intercepts.
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2 solutions
Now, for a function to have a parabola graph, it must be a quadratic function.
Therefore, f ( x ) = x 3 − 3 x + 5 and f ( x ) = 3 x + 9 do not satisfy the conditions.
Next, the graph is a n-shaped parabola, which is something like this:
For quadratic functions f ( x ) = a x 2 + b x + c , a = 0 to have this kind of graph, the coefficient of x 2 must be negative, which is a < 0
Two of the choices satisfies this: f ( x ) = − x 2 − 5 x − 9 and f ( x ) = − 3 x 2 − 2 x + 4
The final condition: The graph has no y -intercept.
Sadly, none of the two choices satisfy this. As long as the domain is defined as D f = ( − ∞ , ∞ ) , it will pass through the y -axis, and there will be a y -intercept.
Therefore, None of the functions given are correct
It is simpler to evaluate f(0).
No y-intercept means at x=0, y has no real value for given condition .
As can be seen, for each function, Df =(−∞,∞) and NO y-intercept , when x=0, y does have a real value.
So no function satisfy this condition.