Respuesta :
Answer:
Step-by-step explanation:
(1) List all possible rational zeros of f:
The possible rational zeros (roots) of a polynomial are given by the factors of the constant term divided by the factors of the leading coefficient. For the given function
+4, the constant term is 4, and the leading coefficient is 1.
Possible rational zeros: ±1, ±2, ±4
(2) Find all rational zeros and determine their multiplicities:
To find the rational zeros, you can use the rational root theorem or synthetic division. If you perform synthetic division with each possible zero, you'll find that there are no rational zeros for this polynomial. In other words, there are no values among ±1, ±2, ±4 that make
(3) Describe the end behavior using arrow notation:
The end behavior of a cubic function is determined by the leading term, which is
in this case. As
x approaches negative or positive infinity,
f(x) also goes to negative or positive infinity. You can describe this as:
x→∞
f(x)=∞
(4) Find coordinates of x-intercepts and the y-intercept:
As mentioned earlier, there are no rational zeros, so there are no x-intercepts among rational numbers. However, you can find x-intercepts using numerical methods or graphing technology. The y-intercept is found by setting
(5) Sketch the graph of f:
Given the information from above, you can sketch the graph. Make sure to mark the y-intercept and any x-intercepts you find.
Please note that for a more accurate graph and to find any non-rational roots or additional features, you might need to use calculus or numerical methods.
