Step-by-step explanation:
the term with the highest exponent determines the behavior of the graph for very, very large positive values of x or very, very low negative values of x (= the end behavior).
a.
f(x) = -0.3x⁴ - 5x² - 3x + 4
the highest exponent is 4. that is even, making x⁴ always a positive number. as the square or the square of squares or ... of negative numbers always delivers positive numbers too.
the factor of -0.3 then turns this always positive number into an always negative number.
as mentioned, the larger the absolute value of x, the more x⁴ drowns out the other terms with lower exponents.
so, the end behavior for f(x) when x going to -infinity and to +infinity is going to -infinity in both cases.
b.
g(x) = 15x⁷ + 4x³ - 3
the highest exponent is 7. that is an uneven (odd) number, making this a positive number for positive x values, and a negative number for negative x values.
the factor 15 keeps the sign of the x⁷ term.
similar to a., the larger the absolute value of x, the more x⁷ drowns out the other terms with lower exponents.
so, the end behavior for g(x) when x is going to +infinity is going to +infinity. and when x is going to -infinity, it is going to -infinity.
