Let the graph of g be a horizontal shrink by a factor of +, followed by a translation 6 units down of the graph of f (x) = x³+ 2x + 4 . Write a rule for g . g(x) :

Q: Describe the translation needed to obtain the graph of g(x) = 7X-9 from the graph of f(x) = 7*.…

A:

Q: Let the graph of g be a vertical shrink by a factor of : 1 followed by a translation 2 units up of…

A:

Q: If f(x) = 2x2 + 5 and g(x) = 3x + a, find a so that the graph of f ∘ g crosses the y-axis at 23.

A: fx=2x2+5  &  gx=3x+a Now, f∘gx=fgx=f3x+a=23x+a2+5

Q: Use the graph of f(x) = √x to obtain the graph of g(x) = √(x - 4)

A: We first graph the parent function  f(x) = √x

Q: Sketch the graphs of g and g 1. Then find the rule for g-x) g(x)=x2+2 (x 20) gx) =

A: Given function is gx=x2+2

Q: Describe the transformations of the graph of f(x) = 2.2x that yield the graph of g(x) = −2.2x + 4.

A: Given functions are: f(x) = 2.2x g(x) = - 2.2x  +4     The red colored graph represents the…

Q: The graphs of f(x) = x² - 4 and g(x) = x2 - 4 are shown. y 8 8 6 fx) = x -4 6 g(x) = x -4| 4 2 2 -2…

A:

Q: If g(x) = VF(x), where the graph of f is shown, evaluate g'(3). %3D

A:

Q: endpoints

A:

Q: Use the graph of f(x) = to sketch the graph of g. %3D g(x) %3D y 10 f(x) = %3D 5 X -4 -2 2. 4 -5 -10

A: Since g(x) is half of f(x) the required graph will shrink just put some values and see to where the…

Q: Q3) Let f(x) = x², draw the graph of (x + 2)², what is type of this shifting and what is the value…

A:

Q: Sketch the graph of g(x) = 2Vx + Vx*. Support your graph by a table as in the lecture.

A:

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: Show that the production function f(x) = - () x³ + 10x² + 5x, –∞<x<∞ has both a concave and convex…

A: Given f(x)=-23x3+10x2+5x, -∞≤x≤∞ Consider the function f and its derivative f' can be differentiated…

Q: The graph of g(x) = logs(-x) is the graph of f(x) = logsx reflected about the %3D

A: We can plot both the graphs to see thatThe blue curve represents the equation y = log5(x) and the…

Q: Consider the function p(x) = 3x +x - 5x and the graph of y = m(x) below.

A: In the question it is asked to calculate the roots of p(x)=3x3+x2-5x and the graph m(x) given in…

Q: 5.) Sketch the graph. f(x) = x³ + x² – x +1 %3D

A: The graph of a polynomial of 3 degree has at most  2 turns and 3 intersections with the x-axis. If…

Q: 5. Sketch the graph of g(x) =- 16-2x-4 by transforming the graph of f(x) = Vx Label all the graphs…

A: Given:                            f(x)=x   To determine:                           g(x)=126-2x-4…

Q: Sketch the graph of f(x)= x2 + 1

A: Given Data The equation of the graph is fx=1x2+1.   The graph of the equation fx=1x2+1 is,

Q: Use the graph of to obtain the graph of g(x)=(x - 3)2-5.

A:

Q: wich is the graph of f(x)=3

A: Given function, f(x)=y=3

Q: If f(x) = 2x2 + 5 and g(x) = 3x + a, find a so that the graph of f ∘ g crosses the y-axis at 23

A: f(x)=2x2+5g(x)=3x+a

Q: Write a rule for g that represents a translation 4 units right and 1 unit down, followed by a…

A: Consider the function  f(x)=e−x

Q: 19. Determine the end behavior of the graph of f(x) = 3x4 + 2x - 5

A:

Q: Let the graph of g be a vertical stretch by a factor of 3, followed by a translation 3 units down of…

A: To sketch: The graph of g(x). Given information: The graph of g(x) is vertical stretch by a factor…

Q: Use the graph of f(x) = |x| to graph g(x) = – |2x|.

A: To obtain the graph of y=-|2x| from that of y'|x| by using a sequence of transformations

Q: If the graph of f(x) is given by 1 Then the graph of is

A: Gien a graph of some function f(x), the graph of the reciprocal function i.e. 1f(x) can be obtained…

Q: For Exercise, determine the vertical asymptotes of the graph of the function. x + 2 3x + 8x – 3 k(x)…

A:

Q: Let the graph of g be a vertical shrink by a factor of , followed by a translation 3 units down of…

A: Given that  fx=3x3+9x To find g(x):

Q: If f(x) = kx' + x² – kx +2, find k such that the graph of f contains the point (2, 12).

A:

Q: Use this graph of g to find the solutions to g(x) = 3.

A: To find: the solution of the g(x)=3 from graph.

Q: Sketch the graph of g(x) =6-2x-4 by transforming the graph of f(x) = Vx Label all the graphs drawn…

A: We have to sketch the given graph.

Q: Use the graphs of f and g to graph h(x) (f + g)(x). (Graph segments with closed endpoints.) y 3 2 1…

A: Finding the graph of (f+g)(x) from the conditions given

Q: Consider the graph of f(x) = 2x-1.

A:

Q: Sketch the graphs of g and g-1. Then find the rule for g(x). g(x)=Dx2+2 (x20) 8(x) =

A: Inverse of function

Q: Sketch the graphs of g and g 1. Then find the rule for g-(x). g(x)=x2+2 (x20) gx) =

A:

Q: 5. The graph of f(x) = x² is given below. Graph -(x).

A: Given graph of function  , f(x)=x2, and we have to draw a graph of -f(x), For graph look at step 2

Q: Let the graph of g be a vertical shrink by a factor of , followed by a translation 5 units up of the…

A:

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: Show that the graph of f(x)= x6+4 is symmetric with respect to the y-axis without actually drawing…

A: Given: f(x) = x6+4 Graph of a function f(x) is symmetric with respect to y-axis is f-x = fx

Q: If g(x) = x2 – 4, where does the graph of the g(x) cross the x-axis? Make a sketch of the graph.

A: Given g(x)=x2-4We know that x2 graph is a prabola

Q: Let the graph of g be a vertical shrink by a factor of , followed by a translation 3 units down of…

A: Here we want to find g(x), given a function f(x) which is a result of vertical shrinkage of required…

Q: Use the graph of f(x) = x2 to graph g(x) = (x + 3)2 + 1.

A: fx=x2 The graph is,

Q: Draw the graph of g(x) = f(x + 2) below. After finishing the graph, click outside the grid to stop…

A: Known fact: The graph of y=fx+a, a&gt;0 can be obtained by shifting the graph y=fx, a units left…

Q: the graph of f(x)=x^2 is transformed to create the graph of g(x)=f(x)-9

A: Use downward shift of graph

Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

A:

Q: Use transformation rules starting with the basic function f(x) = |x| to sketch and Describe the…

A:

Q: Use the graph of f(x) 2 to sketch the graph of g. %3D g(x) = %3D

A: Given,         The graph of fx=2x2 is shown below :