Graphing Other Functions - SAT Subject Test in Math I
Card 0 of 7
Which equation best represents the following graph?
Which equation best represents the following graph?
We have the following answer choices.
The first equation is a cubic function, which produces a function similar to the graph. The second equation is quadratic and thus, a parabola. The graph does not look like a prabola, so the 2nd equation will be incorrect. The third equation describes a line, but the graph is not linear; the third equation is incorrect. The fourth equation is incorrect because it is an exponential, and the graph is not an exponential. So that leaves the first equation as the best possible choice.
We have the following answer choices.
The first equation is a cubic function, which produces a function similar to the graph. The second equation is quadratic and thus, a parabola. The graph does not look like a prabola, so the 2nd equation will be incorrect. The third equation describes a line, but the graph is not linear; the third equation is incorrect. The fourth equation is incorrect because it is an exponential, and the graph is not an exponential. So that leaves the first equation as the best possible choice.
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Which of the graphs best represents the following function?
Which of the graphs best represents the following function?
The highest exponent of the variable term is two (
). This tells that this function is quadratic, meaning that it is a parabola.
The graph below will be the answer, as it shows a parabolic curve.
The highest exponent of the variable term is two (
The graph below will be the answer, as it shows a parabolic curve.
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Where does 
cross the 
axis?
Where does
crosses the 
axis when 
equals 0. So, substitute in 0 for 
:
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Which of the following is an equation for the above parabola?
Which of the following is an equation for the above parabola?
The zeros of the parabola are at 
and 
, so when placed into the formula
,
each of their signs is reversed to end up with the correct sign in the answer. The coefficient can be found by plugging in any easily-identifiable, non-zero point to the above formula. For example, we can plug in 
which gives
The zeros of the parabola are at
each of their signs is reversed to end up with the correct sign in the answer. The coefficient can be found by plugging in any easily-identifiable, non-zero point to the above formula. For example, we can plug in
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Simplify the following expression:
Simplify the following expression:
To simplify, we must first simplify the absolute values.
Now, combine like terms:
To simplify, we must first simplify the absolute values.
Now, combine like terms:
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Which of the following is a graph for the following equation:
Which of the following is a graph for the following equation:
The way to figure out this problem is by understanding behavior of polynomials.
The sign that occurs before the 
is positive and therefore it is understood that the function will open upwards. the "8" on the function is an even number which means that the function is going to be u-shaped. The only answer choice that fits both these criteria is:
The way to figure out this problem is by understanding behavior of polynomials.
The sign that occurs before the
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Define a function 
.
for exactly one real value of 
on the interval 
.
Which of the following statements is correct about 
?
Define a function
Which of the following statements is correct about
Define 
. Then, if 
, it follows that 
.
By the Intermediate Value Theorem (IVT), if 
is a continuous function, and 
and 
are of unlike sign, then 
for some 
. As a polynomial, 
is a continuous function, so the IVT applies here.
Evaluate 
for each of the following values: 
Only in the case of 
does it hold that 
assumes a different sign at both endpoints - 
. By the IVT, 
, and 
, for some 
.
Define
By the Intermediate Value Theorem (IVT), if
Evaluate
Only in the case of
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