
To calculate: The x- and y- intercepts for the equation

Answer to Problem 59E
The x-intercept is
Explanation of Solution
Given information:
The equation
Formula used:
The function is symmetric about the x-axis, when y is replaced by
The function is symmetric about the y-axis, when x is replaced by
The function is symmetric with respect to origin, when y is replaced by
The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.
The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.
Calculation:
It is provided that the equation is
Substitute the point
Substitute the point
Substitute the point
Substitute the point
Construct a table with the values obtained above,
In the coordinate plane plot the points obtained above and connect them through a line.
The graph of the equation is provided below
Recall that the x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.
Substitute
Therefore, x-intercept is 3.
Recall that the y-intercepts are the points on x-axis where the graph of the equation intersects the y-axis.
Substitute
Therefore, y-intercept is
Recall that the function is symmetric about the x-axis, when y is replaced by
Replace y by
The equation is changed. Therefore, the equation
Recall that the function is symmetric about the y-axis, when x is replaced by
Replace x by
The equation is changed. Therefore, the equation
Recall that the function is symmetric with respect to origin, when y is replaced by
Replace x by
The equation is changed. Therefore, the equation
Thus, the x-intercept is
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.arrow_forwardFind the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forwardshow sketcharrow_forward
- Find the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forwardQuestion 1: Evaluate the following indefinite integrals. a) (5 points) sin(2x) 1 + cos² (x) dx b) (5 points) t(2t+5)³ dt c) (5 points) √ (In(v²)+1) 4 -dv ขarrow_forwardFind the indefinite integral. Check Answer: In(5x) dx xarrow_forward
- Find the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forwardHere is a region R in Quadrant I. y 2.0 T 1.5 1.0 0.5 0.0 + 55 0.0 0.5 1.0 1.5 2.0 X It is bounded by y = x¹/3, y = 1, and x = 0. We want to evaluate this double integral. ONLY ONE order of integration will work. Good luck! The dA =???arrow_forward43–46. Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 15.52) the directions of maximum increase, maximum decrease, and no change for f. ■ 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





