Graphing Piecewise and Recusive Functions

Practice Questions

SAT Subject Test in Math II › Graphing Piecewise and Recusive Functions

Questions

Define a function as follows:

$g(x) = \left{\begin{matrix} \sin \frac{x}{2} -1 &x\le - \pi \ \cos 2x & -\pi < x \le 0 \ 1-\tan \frac{x }{2}&0< x < \pi \ 0 & x\ge \pi \end{matrix}\right.$

Give the -intercept of the graph of the function.

Define a function as follows:

$g(x) = \left{\begin{matrix} x^{2}-2x+7 &x\le -1 \ 9-x & -1 < x \le 0 \ x+8 &0< x \le 1 \ x^{2}+3x+ 6& x> 1 \end{matrix}\right.$

At which of the following values of is the graph of discontinuous?

II)

III)

Define function as follows:

$g(x) = \left{\begin{matrix} x^{2}-2x+7 &x\le -1 \ 9-x & -1 < x \le 0 \ x+8 &0< x \le 1 \ x^{2}+3x+ 6& x> 1 \end{matrix}\right.$

Give the -intercept of the graph of the function.

Define a function as follows:

$g(x) = \left{\begin{matrix} x^{2}-6x-7 &x\le -5 \ 6-x & -5 < x \le 0 \ x+6 &0< x \le 5\ x^{2}-x- 6& x> 5 \end{matrix}\right.$

How many -intercept(s) does the graph of have?

Define a function as follows:

$g(x) = \left{\begin{matrix} 6-x &x\le -5 \ x^{2}-6x-7 & -5 < x \le 0 \x^{2}-x- 6 &0< x \le 5\x+6 & x> 5 \end{matrix}\right.$

How many -intercept(s) does the graph of have?

Define a function as follows:

$g(x) = \left{\begin{matrix} \sin \frac{x}{2} -1 &x\le - \pi \ \cos 2x & -\pi < x \le 0 \ 1-\tan \frac{x }{2}&0< x < \pi \ 0 & x\ge \pi \end{matrix}\right.$

At which of the following values of is discontinuous?

I) $x = -\pi$

II)

III) $x= \pi$

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