Solving Piecewise and Recusive Functions

Practice Questions

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

Questions

9

1

Define functions and as follows:

$f(x) = \left{\begin{matrix} 2x+ 1 &x< 0 \ 3x & x \ge 0 \end{matrix}\right.$

$g(x) = \left{\begin{matrix} x+ 9 &x< 0 \ x- 2 & x \ge 0 \end{matrix}\right.$

Evaluate $(f \circ g) \left (-1.7\right )$ .

2

Define and as follows:

$f(x) = \left{\begin{matrix} x+ 2,& x < 0 \ 4-x, & x \geq 0 \end{matrix}\right.$

$g(x) = \left{\begin{matrix} 4x ,& x < 3 \ 3x, & x \geq 3 \end{matrix}\right.$

Evaluate $(f \circ g) \left ( 3\right )$ .

3

Which of the following would be a valid alternative definition for the provided function?

$f(x) = \left | \frac{3}{4} x - \frac{7}{3} \right |$

4

Define two functions as follows:

$f(x) = \begin{Bmatrix} 2x- 7& \textrm{for } x < 0 \ & \ 3x+ 3& \textrm{for } x\ge 0 \end{matrix}$

$g(x) = \begin{Bmatrix} 3x+ 3 & \textrm{for } x < 0 \ & \ 2x- 7 & \textrm{for } x\ge 0 \end{matrix}$

Evaluate $(f \circ g) (5)$ .

5

Define function as follows:

$f(x) = \left{\begin{matrix} 2x- 5 &x< 0 \ -3x & x \ge 0 \end{matrix}\right.$

Give the range of .

6

Define functions and as follows:

$f(x) = \left{\begin{matrix} 2x &x< -1 \ 3x & x > 1 \end{matrix}\right.$

$g(x) = \left{\begin{matrix} x+ 5 &x< -1 \ x- 2 & x > 1 \end{matrix}\right.$

Evaluate Evaluate $(f \circ g)(3)$ .

7

Define functions and as follows:

$g(x) = \left{\begin{matrix} x+ 6 &x< 0 \ x- 3 & x \ge 0 \end{matrix}\right.$

Evaluate $(f \circ g) \left ( 2\frac{1}{3}\right )$ .

8

Define function as follows:

$f(x) = \left{\begin{matrix} x- 7 &x< -1 \ 6-x & x > 1 \end{matrix}\right.$

Give the range of .

9

Define functions and as follows:

$f(x) = \left{\begin{matrix} 2x &x< -1 \ 3x & x > 1 \end{matrix}\right.$

$g(x) = \left{\begin{matrix} x+ 5 &x< -1 \ x- 2 & x > 1 \end{matrix}\right.$

Evaluate $(g \circ f)(-3)$ .

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