Mojo S.

Caltech Graduate

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SAT II Mathematics Level 2

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Question:

If $$f(x) = \frac{5x + 10}{3x + 4}$$, what is the value of $$f(x)$$ as x approaches infinity?

Mojo S.

Answer:

The answer to this question is $$\frac{5}{3}$$. As $$x$$ approaches infinity, the value of the numerator can be approximated as $$5x$$ because the constant, $$10$$, will become very small in comparison. Similarly, as $$x$$ approaches infinity, the value of the denominator approaches $$3x$$. Thus, as $$x$$ approaches infinity, the value of the function approaches $$\frac{5x}{3x}$$. This simplifies to $$\frac{5}{3}$$.

Pre-Calculus

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Question:

Find the domain and range for $$f(x) = \sqrt x$$?

Mojo S.

Answer:

The solution is defined for $$x\ge0$$, so the domain is $$[0,\infty]$$. This function is a monotonically increasing function. This means that if $$ a > b $$ then $$f(a) > f(b) $$. Using the domain, we know that the lowest value this function can take on is $$ f(0) = 0 $$. Because the function continues to increase as $$x$$ increases, the range is not bounded above. So the range is $$[0, \infty]$$.

Pre-Algebra

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Question:

What is 2^5?

Mojo S.

Answer:

The answer for this question is 32. The exponent signs means how many times to multiply the base number by itself. So 2^5 is 2 * 2 * 2 * 2 * 2 = 32, so 5 multiplications of 2.

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