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# Algebra And Functions - Advanced

In the above figure, the graphs of 2 functions $$f(x)$$ and $$g(x)$$ are drawn in the interval from $$x = -2$$ to $$x = 2$$. Which of the following equations could express $$g(x)$$ in terms of $$f(x)$$?

A) $$g(x) = f(x)+1$$
B) $$g(x) = f(x+1)$$
C) $$g(x) = f(x) - 1$$
D) $$g(x) = f(x-1)$$
E) $$g(x) = f(x)$$

If $$n$$ is a positive integer, which of the following is NOT equal to $$\left( 3^9 \right) ^n$$?

A) $$3^{9n}$$
B) $$9 ^ {4.5n}$$
C) $$\left( 3^{3n} \right) \left( 9^{3n} \right)$$
D) $$27^{3n}$$
E) $$\left( 27^{n} \right) \left( 9^{ n} \right)$$

$T(t) = 1000 ( 0.85)^ t$

The above function is used to estimate the population size of tigers. If $$T(t)$$ represents the number of tigers that are alive $$t$$ decades after the year 1950, which of the following is true about the population of tigers from 1970 to 1980?

A) It decreased by approximately 100.
B) It decreased by approximately 200.
C) It decreased by approximately 400.
D) It increased by approximately 100.
E) It increased by approximately 200.

$10 x + m y = - 5$

In the above equation, the slope of the line is $$-5$$. What is the value of $$m$$?

Given that $$x^2 = 2x + 8$$, which of the following statements must be true?

A) $$x = 2$$
B) $$x = 4$$
C) $$x = -2$$
D) $$x^2 < 2x$$
E) $$x^2 > 2x$$

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