Sat practice Test #8 Answer Explanations

Choice B is correct. The x-coordinates of the x-intercepts of the 
graph are –3, 0, and 2. This means that if y = f (x) is the equation of 
the graph, where f is a polynomial function, then (x + 3), x, and (x − 2) 
are factors of f. Of the choices given, A and B have the correct factors. 
However, in choice A, x is raised to the first power, and in choice B, 
x is raised to the second power. At x = 0, the graph touches the x-axis 
but doesn’t cross it. This means that x, as a factor of f, is raised 
to an even power. If x were raised to an odd power, then the graph 
would cross the x-axis. Alternatively, in choice A, f is a third-degree 
polynomial, and in choice B, f is a fourth-degree polynomial. The 
y-coordinates of points on the graph become large and positive as x 
becomes large and negative; this is consistent with a fourth-degree 
polynomial, but not with a third-degree polynomial. Therefore, of the 
choices given, only choice B could be the equation of the graph.
Choice A is incorrect. The graph of the equation in this answer choice 
has the correct factors. However, at x = 0 the graph of the equation in 
this choice crosses the x-axis; the graph shown touches the x-axis but 
doesn’t cross it. Choices C and D are incorrect and are likely the result 
of misinterpreting the relationship between the x-intercepts of a graph 
of a polynomial function and the factors of the polynomial expression.
QUESTION 12
Choice D is correct. Dividing both sides of equation
2a 
_ 
b
 = 1 
_ 
2 by 2 
gives  a 
_ 
b
 = 1 
_ 
4 . Taking the reciprocal of both sides yields 
b 
_ 
a  = 4.
Choice A is incorrect. This is the value of  a 
_ 
2b
, not  b 
_ 
a . Choice B is 
incorrect. This is the value of  a 
_ 
b
 , not  b 
_ 
a . Choice C is incorrect. This is 
the value of  b 
_ 
2a  , not 
b 
_ 
a .

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ANSwER ExPlANATIONS
| SAT Practice Test #8
QUESTION 13