Function Graphs: Level 2 Challenges Practice Problems Online

$\large (X-1)(X-3)(X-5)(X-7)\ldots (X-97) < 0$

How many positive integers $X$ satisfy the inequality above?

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

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

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

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

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

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

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

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

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Function Graphs: Level 2 Challenges