Question

Evaluate the piecewise defined function at the indicated values. $$ \begin{array}{ll}{f(x)=\left\{\begin{array}{ll}{3 x} & {\text { if } x<0} \\ {x+1} & {\text { if } 0 \leq x \leq 2} \\ {(x-2)^{2}} & {\text { if } x>2} \\ {(x-2)^{2}} & {\text { if } x>2}\end{array}\right.} \\ {f(-5), f(0), f(1), f(2), f(5)}\end{array} $$

Name: Problem 30, Chapter 3: Algebra and Trigonometry
Uploaded: 2020-08-10T19:24:37-08:00
Duration: 45 s
Channel: Amy Jiang
Description: Evaluate the piecewise defined function at the indicated values. f(x)={ 3 x if x 2 (x-2)^2 if x>2 . f(-5), f(0), f(1), f(2), f(5)

   Evaluate the piecewise defined function at the indicated values.
$$
\begin{array}{ll}{f(x)=\left\{\begin{array}{ll}{3 x} & {\text { if } x<0} \\ {x+1} & {\text { if } 0 \leq x \leq 2} \\ {(x-2)^{2}} & {\text { if } x>2} \\ {(x-2)^{2}} & {\text { if } x>2}\end{array}\right.} \\ {f(-5), f(0), f(1), f(2), f(5)}\end{array}
$$

Algebra and Trigonometry

James Stewart,… 3rd Edition

Chapter 3, Problem 30

Instant Answer

Solved by Expert Amy Jiang

08/10/2020

Step 1

Since $-5$ is less than $0$, we use the first condition of the piecewise function, which is $3x$. Substituting $-5$ for $x$, we get $3(-5) = -15$. So, $f(-5) = -15$. Show more…

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Evaluate the piecewise defined function at the indicated values. $$ \begin{array}{ll}{f(x)=\left\{\begin{array}{ll}{3 x} & {\text { if } x<0} \\ {x+1} & {\text { if } 0 \leq x \leq 2} \\ {(x-2)^{2}} & {\text { if } x>2} \\ {(x-2)^{2}} & {\text { if } x>2}\end{array}\right.} \\ {f(-5), f(0), f(1), f(2), f(5)}\end{array} $$

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Key Concepts

Piecewise Functions

Piecewise functions are defined by different expressions over different parts of the domain. They allow for multiple functional behaviors in different intervals and are often used to model situations where a function needs to change its formula based on the input value.

Function Evaluation

Function evaluation involves substituting a specific input into a function's expression to compute the corresponding output. When evaluating piecewise functions, it is important to first determine which piece of the function applies to the given input based on the domain conditions.

Conditional Domain Partitioning

Conditional domain partitioning refers to the process of dividing the function's domain into intervals where each interval obeys a specific rule or formula. This concept is crucial in understanding piecewise functions, as the appropriate formula is selected based on the condition that the input satisfies.

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