Answer:
C, E
Explanation:
You want to identify the true statements about the end behavior, symmetry, domain, and range of g(x) = -5x² and f(x) = 5x-10.
End behavior
The function g(x) is of even degree (the exponent is 2), and the function f(x) is of odd degree (the exponent is 1). An even-degree function cannot have the same end behavior as an odd-degree function.
Range
The range of any odd-degree polynomial function is (-∞, +∞).
Any even-degree polynomial function will have a global maximum or minimum so cannot have the same range. The range of g(x) is (-∞, 0].
Domain
The domain of any polynomial function is "all real numbers." Both f and g have the same domain.
Symmetry
An even-degree function may have an axis of symmetry. An odd-degree function cannot be symmetrical about any line. The functions cannot have the same symmetry.
Points of intersection
Two polynomial functions may have a number of points of intersection equal to the highest degree. That means a degree-1 and a degree-2 function may have up to 2 points of intersection. These two functions intersect twice, as the graph in the attachment shows.