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Here is a function of the form f (x) = ab". Which point on the graph immediately tells you the value of a? %3D

Here is a function of the form f (x) = ab". Which point on the graph immediately tells you the value of a? %3D

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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The image contains text and a graph related to a mathematical function. Here's the transcription and description for an educational website: --- ### Understanding the Function \( f(x) = ab^x \) **Question:** Consider a function of the form \( f(x) = ab^x \). Which point on the graph immediately tells you the value of \( a \)? **Graph Explanation:** The graph is plotted on a coordinate plane with horizontal (x-axis) and vertical (y-axis) lines forming a grid. A red curve representing the function is displayed, with a significant point highlighted at the position where it intersects the y-axis. - **Y-axis Intersection:** The curve intersects the y-axis at this point, indicating the value of \( a \) when \( x = 0 \), as \( f(0) = ab^0 = a \). - **Axes:** - The x-axis is labeled but not numbered, suggesting it could represent a range of values. - The y-axis has a marking near its lower end, potentially representing scale or specific value. Understanding the graph’s behavior and this specific intersection point provides insight into the function’s initial value \( a \). ---
Transcribed Image Text:The image contains text and a graph related to a mathematical function. Here's the transcription and description for an educational website: --- ### Understanding the Function \( f(x) = ab^x \) **Question:** Consider a function of the form \( f(x) = ab^x \). Which point on the graph immediately tells you the value of \( a \)? **Graph Explanation:** The graph is plotted on a coordinate plane with horizontal (x-axis) and vertical (y-axis) lines forming a grid. A red curve representing the function is displayed, with a significant point highlighted at the position where it intersects the y-axis. - **Y-axis Intersection:** The curve intersects the y-axis at this point, indicating the value of \( a \) when \( x = 0 \), as \( f(0) = ab^0 = a \). - **Axes:** - The x-axis is labeled but not numbered, suggesting it could represent a range of values. - The y-axis has a marking near its lower end, potentially representing scale or specific value. Understanding the graph’s behavior and this specific intersection point provides insight into the function’s initial value \( a \). ---
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