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Precalculus : Piecewise Functions

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Example Questions

Example Question #1 : Piecewise Functions

Let

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

What does $\displaystyle y$ equal when x=3 $\displaystyle x=3$?

Possible Answers:

$\displaystyle 6$

$\displaystyle 3$

$\displaystyle 10$

$\displaystyle 12$

Correct answer:

$\displaystyle 12$

Explanation:

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

x=3 $\displaystyle x=3$

y=x+9 $\displaystyle y=x+9$

$\displaystyle y=3+9=12$

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Example Question #1 : Piecewise Functions

Let

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

What does $\displaystyle y$ equal when x=0 $\displaystyle x=0$?

Possible Answers:

$\displaystyle 8$

$\displaystyle 0$

$\displaystyle -9$

$\displaystyle 9$

Correct answer:

$\displaystyle -9$

Explanation:

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

y=x-9 $\displaystyle y=x-9$

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

$\displaystyle y=0-9=-9$.

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Example Question #1 : Piecewise Functions

Determine the value of f(1) $\displaystyle f(1)$ if the function is

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

Possible Answers:

f(1)=1 $\displaystyle f(1)=1$

f(1)=3 $\displaystyle f(1)=3$

f(1)=4 $\displaystyle f(1)=4$

$f(1)=\pi$ $\displaystyle f(1)=\pi$

Correct answer:

f(1)=1 $\displaystyle f(1)=1$

Explanation:

In order to determine the value of f(1) $\displaystyle f(1)$ of the function we set x=1. $\displaystyle x=1.$

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

f(1)=1 $\displaystyle f(1)=1$

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Example Question #1 : Piecewise Functions

Determine the value of f(1) $\displaystyle f(1)$ if the function is

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

Possible Answers:

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

f(1)=3 $\displaystyle f(1)=3$

f(1)=1 $\displaystyle f(1)=1$

f(1)=3 $\displaystyle f(1)=3$

Correct answer:

f(1)=1 $\displaystyle f(1)=1$

Explanation:

In order to determine the value of f(1) $\displaystyle f(1)$ of the function we set x=1. $\displaystyle x=1.$

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

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

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Example Question #1 : Piecewise Functions

For the function f(x) $\displaystyle f(x)$ defined below, what is the value of f(x) $\displaystyle f(x)$ when x=3 $\displaystyle x=3$?

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

Possible Answers:

-2

Correct answer:

Explanation:

Evaluate the function for x=3 $\displaystyle x=3$. Based on the domains of the three given expressions, you would use $2^{x}$ $\displaystyle 2^{x}$, since $\displaystyle x$ is greater than or equal to $\displaystyle 3$.

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

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Precalculus : Piecewise Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Piecewise Functions

Example Question #1 : Piecewise Functions

Example Question #1 : Piecewise Functions

Example Question #1 : Piecewise Functions

Example Question #1 : Piecewise Functions

All Precalculus Resources

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