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,2 { +х +a, х< -2 x < -2 f (x) = x > -2

,2 { +х +a, х< -2 x < -2 f (x) = x > -2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

Find a value for a so that the function f(x) is continuous 

 

a=-10

a=2

a=-6

a=-8

The image shows a piecewise function \( f(x) \) defined as follows: \[ f(x) = \begin{cases} x^2 + x + a, & \text{if } x < -2 \\ x^3, & \text{if } x \geq -2 \end{cases} \] This function is divided into two parts: 1. For \( x < -2 \), the function is given by the quadratic expression \( x^2 + x + a \). 2. For \( x \geq -2 \), the function is given by the cubic expression \( x^3 \). There are no graphs or diagrams accompanying the function in the image.
Transcribed Image Text:The image shows a piecewise function \( f(x) \) defined as follows: \[ f(x) = \begin{cases} x^2 + x + a, & \text{if } x < -2 \\ x^3, & \text{if } x \geq -2 \end{cases} \] This function is divided into two parts: 1. For \( x < -2 \), the function is given by the quadratic expression \( x^2 + x + a \). 2. For \( x \geq -2 \), the function is given by the cubic expression \( x^3 \). There are no graphs or diagrams accompanying the function in the image.
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