×
Back to all chapters

# Function Graphs

Graphs are visual representations of functions. If you know how to read graphs, you can say a lot about a function just by looking at its graph. Learn this fine art of mathematical divining.

# Function Graphs: Level 2 Challenges

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

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.

$\left| 1-\left| 1-\left| x-1 \right| \right| \right| =\alpha$

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.

×