For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and only if the point (x, -y) lies on the curve. Explain why a curve that is symmetric about the x-axis is not the graph of a function, unless the function is y = 0.

Q: For the function y = (x − 2) In x, what are the two x intercepts, and between the two intercepts, is…

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x2, (0, 8)…

A: It is given that, fx=x2, 0,8. Any point on the given curve will be in the form x,y=x,x2. Distance…

Q: Find the slope of the secant line to the function f(x)=4x²- 3x, through point P, where x= - 1, and…

A: To find the slope of secant line PQ to  the function f(x)

Q: What are the x- and y-intercepts of a function, and how are they found?

A: The x-intercept is the length from origin to where the graph of the function cut the x-axis.   The…

Q: a) Find the points on the graph of f(x) = 2x- 3r²- 12x + 8 where the tangent is 3. horizontal.

A:

Q: You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller…

A: Given the perimeter (or) Total length of fencing is 1000 ftFrom the given figure total length of…

Q: List the x-values in the graph at which the function is not differentiable. 3 -2 - 1 1 3,

A:

Q: Suppose the slope of the curve y = f'(x) at (4, 7) is §. Find f'(7).

A: Given slope of the curve y=f-1(x) at (4,7) is 45

Q: Find the points on the graph of the function that are closest to the given point. f(x)=x², (0, 9)…

A: Given function is fx=x2  and the point is 0, 9   To Find: The points on the graph of the function…

Q: List the x-values in the graph at which the function is not differentiable. -3

A: In this question with the help of graph theory we have to find the points where function is not…

Q: Use the vertical line test to identify graphs in which y is a function of x.

A:

Q: Use the vertical line test to identify graphs in which y is a function of x.

A: The given graph is

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

A:

Q: Which of the functions has the y-axis as the line of symmetry?

A: Generally we check three kinds of symmetries for the graphs. Symmetry about X axis Symmetry about Y…

Q: Find the points on the graph of the function that are closest to the given point. Rx) - х2, (0, 7)…

A: A detailed solution is given below.

Q: The equilateral trianhle is inscribed in a circle of radius 6r. Express the area A within the circle…

A:

Q: List the points in the graph at which the function is not differentiable.

A:

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: use the concepts of translation and/or reflection to describe how the second curve can be obtained…

A: To explain: How the second curve fx=-x+8 is obtained form the first curve fx=x by using the concept…

Q: at is the graph of the function

A: Given that: f(x)=4-xx+2

Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: Find Domain and range of f(x)=x^x and graph it.

A: The objective is to find Domain and range of f(x)=x^x and graph it.

Q: Match the function with the graph of its end behavion

A: We are given with the graph we have match and behavior of graph

Q: A rectangular piece of cardboard is 4 times as long as it is wide. shorter side is y inches and an…

A:

Q: The hypotenuse of an isosceles right triangle is to be made into a circle C. Express the area A of C…

A:

Q: Find the points on the graph of the function that are closest to the given point. F(x)=x², (0, 9)…

A: f(x)=x^2, (0,9)

Q: Can every curve in the coordinate plane be the graph of a function? Why?

A: Question- Can every curve in the coordinate plane be the graph of a function ? why? Answer- A…

Q: sketch the graph of the function f(x, y) = sqrt(4-4x^2-y^2)

A: Given function is, f(x,y) = 4-4x2-y2

Q: Find the points of inflection and discuss the concavity of the graph of the function f(x)= x +…

A:

Q: What will be the orientation of the curve of the graph of the function f(x) = on (-3,0)? A.…

A:

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x, (0, 2)…

A:

Q: Sketch the graph of the function. y = (1/3)ex

A: GIven:y=13ex To draw its graph.

Q: Supposed that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions…

A: Given Data: The number of females in the US under 18 is: N=0.140x+36.4 The slope of the graph of the…

Q: List the points in the graph in the interval 1 <x<7 at which the function is not differentiable 18-

A:

Q: The graph of f- is a reflection of the graph of f about the line whose equation is y = x. y 0. x 0.…

A: We want the inverse of function by reflection

Q: Graph the function as a solid curve 1) f(x) =극지•3

A: We have to graph

Q: Prove that the only function whose graph is symmetric with respect to both the y-axis and the origin…

A:

Q: 1) Determine whether the equation defines y as a function of x. x = y3

A: Givenx=y3

Q: Sketch the graph of the function over the indicated interval plot two exact points. y = 2tan( 7x-),…

A: to sketch the graph of the function

Q: find all the values of x at which the curve has a slope of -1. f(x) = 5 +x -3x^2

A: Given function, fx=5+x-3x2 And slope = - 1 i. e. f'x=-1

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x2, (0, 4)…

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) - х2 - 2, (0,…

A:

Q: Please

A:

Q: List the points in the graph in the interval -1<x<7 at which the function is not differentiable.

A:

Q: Find the are of the left half of the curve of the function r = 3-2sin(θ).

A: