Piecewise Functions - Pre-Calculus

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Question

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

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

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Answer

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 .

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

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Question

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

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

Tap to reveal answer

Answer

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 .

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

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Question

Let

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

What does equal when ?

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Answer

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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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Question

Determine the value of if the function is

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

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Answer

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

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Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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

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Question

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

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

Tap to reveal answer

Answer

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 .

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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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Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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

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Question

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

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

Tap to reveal answer

Answer

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 .

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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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Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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

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Question

Let

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

What does equal when ?

Tap to reveal answer

Answer

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

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

.

← Didn't Know|Knew It →

Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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Question

Determine the value of if the function is

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

Tap to reveal answer

Answer

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

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

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Knew It

Piecewise Functions - Pre-Calculus

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

Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .

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

Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .

Let What does equal when ?

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

Let What does equal when ?

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

Let What does equal when ?

Because we use the first equation. Therefore, plugging in x=0 into the above equation we get the following, .

Determine the value of if the function is

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

Determine the value of if the function is

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

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

Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .

Let What does equal when ?

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

Let What does equal when ?

Because we use the first equation. Therefore, plugging in x=0 into the above equation we get the following, .

Determine the value of if the function is

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

Determine the value of if the function is

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

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

Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .

Let What does equal when ?

Because we use the first equation. Therefore, plugging in x=0 into the above equation we get the following, .

Determine the value of if the function is

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

Determine the value of if the function is

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

Let What does equal when ?

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

Let What does equal when ?

Because we use the first equation. Therefore, plugging in x=0 into the above equation we get the following, .

Determine the value of if the function is

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

Determine the value of if the function is

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

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

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

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 .

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

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

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

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 .

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

Let

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

What does equal when ?

Let

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

What does equal when ?

Let

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

What does equal when ?

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

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

.

Determine the value of if the function is

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

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

Determine the value of if the function is

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

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

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

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

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

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 .

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

Let

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

What does equal when ?

Let

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

What does equal when ?

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

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

.

Determine the value of if the function is

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

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

Determine the value of if the function is

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

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

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

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

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

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 .

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

Let

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

What does equal when ?

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

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

.

Determine the value of if the function is

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

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

Determine the value of if the function is

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

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

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

Let

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

What does equal when ?

Let

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

What does equal when ?

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

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

.

Determine the value of if the function is

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

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

Determine the value of if the function is

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

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

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