Algebra

Function Graphs

Function Graphs: Level 2 Challenges

         

(X1)(X3)(X5)(X7)(X97)<0\large (X-1)(X-3)(X-5)(X-7)\ldots (X-97) < 0

How many positive integers XX satisfy the inequality above?

Determine whether the function f(x)=ln(x+1+x2)f(x) = \ln(x+ \sqrt{1+x^2} ) is an odd function or an even function.

11x1=α\left| 1-\left| 1-\left| x-1 \right| \right| \right| =\alpha

Find the value of α\alpha for which this equation has exactly 4 distinct solutions. If the value of α\alpha is AA, then find 2A2A.

Find the area of the region bound by the equation x+2y+2xy=10|x+2y|+|2x-y|=10

Given the graph y=lnx y = \ln x , which of these statements describes the transformations to get the graph of y=ln(4x2+4x+1) y = \ln (4x^2 + 4x + 1) for x>12 x > - \frac{1}{2} ?

(1)\quad \text{(1)} Translate to the left by 1 and up by ln4 \ln 4 , then scale vertically by 2.

(2)\quad \text{(2)} Translate to the left by 12\frac{1}{2} and up by ln2 \ln 2 , then scale vertically by 2.

(3)\quad \text{(3)} Translate to the left by 1 and up by ln2 \ln 2 , then scale vertically by 2.

(4)\quad \text{(4)} Translate to the left by 12 \frac{1}{2} and up by ln4 \ln 4 , then scale vertically by 2.

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