/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 Determine the intercepts of the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 13

Determine the intercepts of the graphs of the following equations. $$f(x)=5$$

Short Answer

Expert verified
y-intercept: (0, 5); no x-intercepts.

Step by step solution

01

Understand the Definition of Intercepts

Intercepts are the points where the graph of the equation crosses the x-axis or y-axis. To find intercepts, set the opposite variable to zero.
02

Find the y-Intercept

To determine the y-intercept, set x to 0 and solve for y. For the equation \[f(x) = 5\], it can be written as \[y = 5\]. When x = 0, \[y = 5\]. Thus, the y-intercept is (0, 5).
03

Determine the x-Intercept

For the x-intercept, set y to 0 and solve for x. The equation is \[5 = y\]. Since y is always 5 and never 0, there are no x-intercepts, as the line never crosses the x-axis.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

x-intercept
The x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the value of y is zero. To find it, we set y to 0 in the equation and solve for x. In the given exercise, the equation is $$f(x) = 5$$. By rewriting it, we get $$y = 5$$. Here, y is always 5 and never zero. Therefore, there is no x-intercept for this graph. The line does not cross the x-axis.
y-intercept
The y-intercept is where the graph crosses the y-axis. At this point, the value of x is zero. To find the y-intercept, set x to 0 in the equation. For the equation $$f(x) = 5$$, we write it as $$y = 5$$. When x = 0, $$y = 5$$. Thus, the y-intercept is $$(0, 5)$$. This indicates that the graph crosses the y-axis at the point (0, 5).
graph of a function
The graph of a function is a visual representation of the relationship between the input (x-variable) and the output (y-variable). For the function $$f(x) = 5$$, the output is always 5, regardless of the input value. This results in a horizontal line on the graph. Here are key points about the graph:
  • It is a straight horizontal line parallel to the x-axis.
  • It passes through the y-axis at y = 5.
  • There is no x-intercept as the line never crosses the x-axis.
Understanding these characteristics will help in visualizing and interpreting the graph accurately.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Evaluate \(f(4)\). $$f(x)=x^{0}$$

Evaluate \(f(4)\). $$f(x)=x^{-1}$$

Evaluate \(f(4)\). $$f(x)=x^{3 / 2}$$

Convert the numbers from graphing calculator form to standard form (that is, without E). $$5 E-5$$

Find the points of intersection of the graphs of the functions. (Use the specified viewing window.) $$f(x)=2 x-1 ; g(x)=x^{2}-2 ;[-4,4] \text { by }[-6,10]$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.