Question
(03.03 MC) Given f(x)=(x-1)(x+2)(x-3) what are the zeros and end behavior of the function? -1 2. -3 continues downward to the left and upward to the right -1 2. -3 continues upward to the left and downward to the right 1,-2,3 continues downward to the left and upward to the right 1,-2,3 continues upward to the left and downward to the right
Solution
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(164 Votes)
Ulysses
Elite ยท Tutor for 8 years
Answer
### C.
continues downward to the left and upward to the right
Explanation
## Step 1: Finding the Zeros### To find the zeros of the function
, set
equal to zero and solve for
. This means setting each factor equal to zero:
,
, and
.## Step 2: Solving for x### Solving each equation gives us the zeros:
,
, and
. Therefore, the zeros are 1, -2, and 3.## Step 3: Determining End Behavior### The degree of the polynomial is 3 (since it's a product of three linear factors), which is odd. The leading coefficient is positive (since expanding the expression would result in a positive
term). An odd degree with a positive leading coefficient means the graph goes down to the left and up to the right.