Match the function with its graph. I II y 1 III IV (a) f(x) = x2 ---Select--- (Б) f(x) = x3 ---Select--- %3D (c) f(x) = Vx ---Select--- (d) f(x) = |x| ---Select---
Match the function with its graph. I II y 1 III IV (a) f(x) = x2 ---Select--- (Б) f(x) = x3 ---Select--- %3D (c) f(x) = Vx ---Select--- (d) f(x) = |x| ---Select---
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Match the Function with its Graph
In this exercise, you are given four graphs, each representing a different mathematical function. Your task is to match each function with the correct graph. The functions and graphs are labeled as follows:
#### Functions:
- (a) \( f(x) = x^2 \)
- (b) \( f(x) = x^3 \)
- (c) \( f(x) = \sqrt{x} \)
- (d) \( f(x) = |x| \)
#### Graphs:
- **Graph I**
- **Graph II**
- **Graph III**
- **Graph IV**
Below are detailed descriptions of each graph to help you identify the corresponding functions:
#### Graph I
Graph I shows a curve that starts at the origin (0,0) and rises gradually to the right. This curve indicates a function where the rate of increase in y values starts off slowly and increases as x increases.
#### Graph II
Graph II presents an S-shaped curve that passes through the origin. The curve dips below the x-axis for negative values of x and rises steeply above the x-axis for positive values of x.
#### Graph III
Graph III displays a V-shaped graph with its vertex at the origin (0,0). The graph is symmetrical about the y-axis, with the lines extending linearly upwards in both the positive and negative x directions.
#### Graph IV
Graph IV features a parabola opening upwards with its vertex at the origin. The curve rises symmetrically on either side of the y-axis as x moves away from 0 in both directions.
Use these descriptions to match each function with its corresponding graph:
- (a) \( f(x) = x^2 \) matches with
- (b) \( f(x) = x^3 \) matches with
- (c) \( f(x) = \sqrt{x} \) matches with
- (d) \( f(x) = |x| \) matches with
Select the appropriate graph for each function from the dropdown menus provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F429fd668-1075-4973-8e47-64e8dad266df%2F4348071f-23ab-4941-9ba1-19b5da60d37f%2F26yiq8f_processed.png&w=3840&q=75)
Transcribed Image Text:### Match the Function with its Graph
In this exercise, you are given four graphs, each representing a different mathematical function. Your task is to match each function with the correct graph. The functions and graphs are labeled as follows:
#### Functions:
- (a) \( f(x) = x^2 \)
- (b) \( f(x) = x^3 \)
- (c) \( f(x) = \sqrt{x} \)
- (d) \( f(x) = |x| \)
#### Graphs:
- **Graph I**
- **Graph II**
- **Graph III**
- **Graph IV**
Below are detailed descriptions of each graph to help you identify the corresponding functions:
#### Graph I
Graph I shows a curve that starts at the origin (0,0) and rises gradually to the right. This curve indicates a function where the rate of increase in y values starts off slowly and increases as x increases.
#### Graph II
Graph II presents an S-shaped curve that passes through the origin. The curve dips below the x-axis for negative values of x and rises steeply above the x-axis for positive values of x.
#### Graph III
Graph III displays a V-shaped graph with its vertex at the origin (0,0). The graph is symmetrical about the y-axis, with the lines extending linearly upwards in both the positive and negative x directions.
#### Graph IV
Graph IV features a parabola opening upwards with its vertex at the origin. The curve rises symmetrically on either side of the y-axis as x moves away from 0 in both directions.
Use these descriptions to match each function with its corresponding graph:
- (a) \( f(x) = x^2 \) matches with
- (b) \( f(x) = x^3 \) matches with
- (c) \( f(x) = \sqrt{x} \) matches with
- (d) \( f(x) = |x| \) matches with
Select the appropriate graph for each function from the dropdown menus provided.
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