SAT Mathematics Practice Test 4

Question : 32 of 58

Marks: +1, -0

In the

xy-

plane, the graph of function f has x-intercepts at

−3, −1,

and

1

. Which of thefollowing could define

f

$f(x )=(x−3)(x−1)(x+1)$
$f(x )=(x−3)(x−1)^2$
$f(x )=(x+1)(x−1)(x+3)$
$f(x)=(x+1)^2(x+3)$

Validate

Solution:

All of the given choices are polynomials. If the graph of a polynomial function f in the xy-plane has an x-intercept at b, then

(x−b)

must be a factor of

f(x)

. Since

−3, −1

, and 1 are each x-intercepts of the graph of f, it follows that

(x+3),(x+1),

and

(x−1)

must each be a factor of

f(x)

.The factored polynomial function in choice C is the only polynomial given with these 3 factors.
Choices A, B, and D are incorrect because they do not contain all three factorsthat must exist if the graph of the polynomial function f has x-intercepts at

−3, −1,

and

1.

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