Piecewise Functions

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Pre-Calculus › Piecewise Functions

Questions 1 - 5

1

Let

$y=\left{\begin{matrix} 2x&x\leq 0\ x+9& x>0 \end{matrix}\right.$

What does equal when ?

Explanation

Because 3>0 we plug the x value into the bottom equation.

2

For the function defined below, what is the value of when ?

$f(x)=\left{\begin{matrix} -x+1&\text{ for }x<1\ x^{2}-2&\text{ for }1< x< 3\ 2^{x}&\text{ for }x\geq 3 \end{matrix}$

8

7

3

0

-2

Explanation

Evaluate the function for . Based on the domains of the three given expressions, you would use $2^{x}$ , since is greater than or equal to .

$2^{x}=2^{3}=8$

3

Determine the value of if the function is

$f(x)=\left{\begin{matrix} x& x<3\ \pi&x=3 \ 4&x>3 \end{matrix}\right.$

$f(1)=\pi$

Explanation

In order to determine the value of of the function we set

The value comes from the function in the first row of the piecewise function, and as such

4

Determine the value of if the function is

$f(x)=\left{\begin{matrix} \sqrt{x}& 0\leq x<4\ \3&x=4 \ e^{-x}&x>4 \end{matrix}\right.$

$f(1)=\frac{1}{e}$

Explanation

In order to determine the value of of the function we set

The value comes from the function in the first row of the piecewise function, and as such

$f(1)=\sqrt{1}=1$

5

Let

$y=\left{\begin{matrix} x-9&x\leq 0\ x+9& x>0 \end{matrix}\right.$

What does equal when ?

Explanation

Because $0\leq0$ we use the first equation.

Therefore, plugging in x=0 into the above equation we get the following,

.

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