12. Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of the function:f (x) = 2x³ – x² +1 - Even, y-axis symmetry Odd; origin symmetry Neither; no symmetry

Q: Determine the vertex and the axis of symmetry of the graph of the function. 1.    f(x) = −2(x + 3)2…

A:

Q: 7. Sketch the graph of a function that satisfies all of the following conditions. is an even…

A: Note that there are many possibility to draw the graph that satisfy all the given conditions.

Q: The graph of y = f(x) is graphed below. What is the end behavior of f (x)? 30000 20000 10000 -10 -8…

A: Given: The graph of the function y=fx is To find: The end behavior of fx.

Q: 1. Let X be the graph of f(x) = x2/3 given below

A: Sol

Q: 5. 5) For the function below, give all the important information about its graph. f(x) = 8 -csc(14x…

A:

Q: 5. Use the equation to classify the function as odd, even, or neither. g(x) = 4x3- x %3D

A:

Q: P2- Graph the fellowing functions. 4ー× xS f cx) 2 2 a- X + 2X メ>! Xく。 gcx) = b-

A:

Q: 10. Find the domain, range of the set of piecewise defined function and graph x<2 4- x, f(x) = l1+…

A:

Q: 11. Find the zeros, multiplicity, y-intercept, and end behavior of f(x) = x(x – 3)(x – 2) then…

A: To find- Find the zeros, multiplicity, y-intercept, and end behavior of fx = xx - 3x - 2 then sketch…

Q: True or False? For a function g(x). g"(3) = -8 indicates that g(x) is at x=3.

A: Given that for a function g(x), g"(3)=-8 indicates that g(x) is................ at x=3

Q: Q1// Graph and discuss, with detail, the continuity of the function -1 <x< 0 x2- 1 2x 0 <x< 1 y =…

A: The given function is y=fx=x2-1,-1≤x&lt;02x,0&lt;x&lt;11,x=1-2x+4,1&lt;x&lt;20,2&lt;x&lt;3

Q: - 5. Sketch the graph of f(x)= x² – 5x + 6 using the Vertex and the X-intercept. Identify the axis…

A: Explanation of the answer is as follows

Q: Sketch the graph of the function f(x) = 3x + 4, its inverse, and the line of symmetry. All three…

A:

Q: -9x+10 2. Let f(x) = Determine if the function is continuous and show the graph of the function. x-2

A: Let's find.

Q: 3 -x'+8 As x→-0, f(x) → ), and as x→0, f(x) → |

A:

Q: Explain why the function is discontinuous at the givennumber a . Sketch the graph of the function.

A: The given function is fx=1x+2if x≠-21if x=-2. Note that limx→-2fx does not exist. This implies that…

Q: 10. Graph the function. f(x) = -2(x- 4)(x + 2) %3D

A: Topic = Parabola

Q: Q#3. For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and…

A: If a curve is symmetric about the x-axis, the points (x,y) and (x,-y) mustlie on the curve. Hence,…

Q: Find the maximum or minimum value of the function.

A: Given fx=3-x-12x2

Q: 2. f(x) = 3[ x]

A:

Q: 5) Identify the leading term, then use the leading term to determine the en graph of the function…

A: Here we have to find the leading term and end behavior of the graph of the functions.

Q: which statements are always true for the graph of a cubic function?  I) When the graph has exactly…

A:

Q: , Consider the function f(x) whose graph is a parabola with a hole in it. Give the equation of this…

A:

Q: Explain why the function is discontinuous at the givennumber a . Sketch the graph of the function.

A: Any function f is continuous at 'a' if 1) f(a) is defined. 2) limx→af(x) exist. 3) limx→af(x)=f(a)

Q: x2 – 3 y = 2х — 4

A:

Q: 12. Sketch a picture of a graph y = f(x) that satisfies f'(-1) > 0, f'(0) = 0 and f'(1) < 0.

A: Follow the procedure given below

Q: (1+ 3x X 1

A:

Q: Sketch the graph of f(x) by hand and use your sketch to find the absolute and local maximum and…

A: Graph of f(x) is as follows :

Q: Sketch the graph of the function. Label the intercept(s) and asymptote(s). x2 9) f(x) x2 - x - 12

A: on solving this we get

Q: List the x-values in the graph at which the function is not differentiable. 2 3. x = 0, x = 3 X = 3…

A:

Q: (2) (a) Find the points of inflection and discuss the concavity of the graph of the function f(x)…

A:

Q: %3D Let X be the graph of f(x) = x2/3 given below

A: Follow the steps.

Q: Sketch a graph of the functionf(x) = −x 3 + 4x 2 − 9x + 3 using the following steps. d) Sketch the…

A: The functions f(x)=-x3+4x2-9x+3. We have to sketch the graph of this function using the steps... 1.…

Q: 3. Explain the transformations of g(x) = 3(x + 5)² + 10 that are needed from the graph of f(x) = x?

A: Given: the function gx=3x+52+10 and fx=x2, To find: The transformations of gx that are needed from…

Q: 6. Sketch the graph of f(x) = (x – 3)(x + 2) (x + 5) using the %3D zeros and end behaviours.

A: Solution is here

Q: 9) Sketch the graph of the piecewise function below. 4 IS-7 -7 3

A:

Q: x - 2x +4x–8 Draw a graph of the function R(x) = Justify all major features using limits. x -11x+18

A: To solve the following problem

Q: 1) Discuss the concavity of the graph of f (2) = #* – 2æª + 1 Show Graph. and find its points of…

A: We can use the application of derivative in order to get the solution. Inflection point at…

Q: 3. Identify the vertical and horizontal asymptotes of the function: f(x) = %3D (x -3)² x2 -4x -5

A:

Q: 13. Use the idea of transfr-mation to sketch the function y = -2f(x+2) + 3 if the graph of y = f(x)…

A: Given: The graph of y=f(x) is

Q: 2A.6A: analyze the effect on the graphs of f(x) = x, when f(x) is replaced by af(x), f(bx), f(x -…

A:

Q: 9. Sketch the graph of the function y = Va + 2 and determine the domain and range.

A: We have to draw the graph

Q: Use the graph of f(x) = 5. to sketch the graph of g. %3D g(x) = %3D x - 8

A: Now, the center of g(x) shifted to 8x -axis. The graph of g(x) , curve will be drawn between the…

Q: 9. Graph the piecewise function: 2 xS-1 h(x) = { x' -1<x< /2 %3D 43

A: We have to graph the function.

Q: Determine the vertex form of the function f : R → R, f(x) = x2 − 4x + 6 and sketch its graph

A:

Q: True or false: The graph of f(x) = (x + 5)2 + 3 has its vertex at (5, 3)._______

A: For  f(x)=a(x-h)2+k, vertex is (h,k)

Q: 3) Classify the type of the fixed points of the function : f(x) = x³

A:

Q: Find f -1(x) . (b) Sketch the graphs of f and f-1 on the same coordinate plane.

A: Given- fx=10-15x To Find- The inverse function f-1x and sketch the graph of fx and f-1x.

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.