In Exercises 67 - 70 , use the following function. f ( x ) = { 2 - x , x ≤ 1 ( x )

Name: Problem 70, Chapter 2: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2019-05-15T05:34:01-08:00
Duration: 1 min
Channel: Sooyeon Kim
Description: In Exercises 67 - 70 , use the following function. f ( x ) = { 2 - x , x ≤ 1 ( x )/( 2 ) + 1 , x > 1 . Multiple Choice What is the value of f ( 1 ) ? (A) 5/ 2 (B) 3/ 2 (C) (D) 0 1(E) does not exist

step 1 Question 70 asks you to use the following function right here, and what is the value of F of 1?

Question

In Exercises $67 - 70$ , use the following function. $f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$ Multiple Choice What is the value of $f ( 1 ) ?$ (A) 5$/ 2 \quad$ (B) 3$/ 2 \quad$ (C) (D) 0 1(E) does not exist

   In Exercises $67 - 70$ , use the following function.

$f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$

Multiple Choice What is the value of $f ( 1 ) ?$

(A) 5$/ 2 \quad$ (B) 3$/ 2 \quad$ (C) (D) 0 1(E) does not exist

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 3rd Edition

Chapter 2, Problem 70

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Solved by Expert Sooyeon Kim

05/15/2019

Step 1

The function is defined as $f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$. Show more…

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In Exercises $67 - 70$ , use the following function. $f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$ Multiple Choice What is the value of $f ( 1 ) ?$ (A) 5$/ 2 \quad$ (B) 3$/ 2 \quad$ (C) (D) 0 1(E) does not exist

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Key Concepts

Piecewise Functions

Piecewise functions are mathematical functions that have different expressions or formulas defined for different intervals of the domain. Each piece is applicable only when the input satisfies its corresponding condition, and understanding which part of the function to use is key to proper evaluation.

Domain Partitioning

Domain partitioning involves dividing the domain of a function into segments based on specific conditions or inequalities. This determines which formula or rule of a piecewise function should be applied when evaluating it at a given input.

Evaluation at Boundary Points

Evaluation at boundary points requires careful attention to the conditions that define each piece of the function. When an input lies exactly on the boundary, the condition that includes equality is used, making correct interpretation of these conditions critical to arriving at the proper function value.

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