Consider the following graph. V(G) = {v1, v2, v3, v4},  e(G) = {e1, e2, e3, e4, e5, e6}, E(G) = {(e1,[v1,v2]),(e2,[v2,v3]),(e3,[v3,v4]),(e4,(v4,v1)), (e5,[v2,v4]), (e6,[v1,v3])} Draw a picture of the graph on scratch paper to help you answer the following two questions. 1. How many paths exist from v1 to v4? 2. What is the length of the longest trail from v1 to v4?

Q: Consider the following graph, where

A: Given,

Q: Use shifting graph to sketch a) y = |(x – 2)² – 1|+1 b) y = 2 – 5sin (3x) -

A: We have to graph the functions by using shifting... a. y=x-22-1+1b. y=2-5sin3x

Q: Select the correct graph for the linear function f(x) which satisfies both f(0) = -2 and f(3) = -2.…

A: We are authorised to solve only one question, please repost remaining questions Graph of function

Q: . Sketch the graph of y = m(x) in Figure 2. FIGURE 2. Graph of y = m(x) r- 3, rS-1 m(x) = 1< x < 5 2

A:

Q: Find an equation for the graph sketched below 7. 4 2. -5-4 -3 -2 -1 2 3 4 5 -2 -3 -4 -5 -6 -7. -8+…

A: We have to find the equation for the graph sketched.

Q: 5] Sketch the graph of r(t) = and show the direction of increasing t.

A: Sin(t) is increasing function from 0 to 90 degree. So that t will increase in the anticlockwise…

Q: Which of the following is NOT true of the graph of ? 6 5 4 3 2+ 1+ 1 3 4 5 6 9 10 -1 -2 -

A: Given graph of y = f(x) Since f(x) = 0 for some x so the function has vertical asymptote

Q: Draw the graph of f(x) 6" -1 10+ 7- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1, I 2 3. 4 5 6 7 8 9 16 -2 -3 -D4…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Draw the graph of f(z) = 6²-4 10 9. 10 -9 -8 -7 -6 -3 -4 -3 -2-1

A: We will draw table of values for particular x and will draw approximate nature of curve

Q: The graph of y f(z) is graphed below. What is the end behavior of f(z)? %3D 15000 10000 5000 -10 -2…

A:

Q: Use shifting graph to sketch a) y = 2 - |V3 – x| b) y = -1+5cos (x – n)

A: A function can be plotted using the basic graphs of the function. The function shifts vertically if…

Q: Which of the following is the graph of (x+3)² + (y+4)² =257 -10-74444 -10-0744 T a . - → 7 "

A:

Q: Which of the following is the graph of * 4x2 + 13y2 52 %3D 12 V 10 4W2 W2 VF -1412-10 -8-6 -4 -2 olc…

A:

Q: Which of the following graphs represents x = -3?

A: Question: Which of the following graph represent x= -3 ?

Q: Consider the graph of f. y 4 3 1 1 2 2 3 4 5 6 7 8 9

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Q: Given the graph of y = f(x), sketch the graph of the transformation y=-f* )+3. 10 -6 -4 -2 -6 -8 -10…

A: We have to sketch graph for the given transformation.

Q: Produce a table for t = 0, 1 ,2 ,3, 4, and 5 and graph the function N, = 3'. 3 4 2.

A: Since there are two questions posted, we will answer the first question posted. If you want the…

Q: Use the graph of y = Ca" to determine C and a. C=

A: Given y = Cax Graph of y = Cax is passing through the points (0,1) and (1,4)

Q: The graph of Y = = Vx is given below: 5- 4 -5 -4 -3 -2 -1 1 2 3 4 5 3.

A:

Q: Plot the appropriate Graph. Here, objective is to show the linear relationship between the sales of…

A: The appropriate graph for two continuous variables to know the linear relationship is scatterplot.

Q: Show that for any planar graph, v-e+f=2. v=vertices e=edges f=faces

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Q: What happens to a graph when a is less than 0?

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Q: Given the following graph, determine the following: f(-4) (6,5), 14) (-4,2) (6,2) -4 -2 6. -2 9(1…

A: Given query is to find the f(-4) from the graph.

Q: Sketch the graphs of f(x) = 2* and g(x) = 3(2*). y y 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5…

A:

Q: Which of the following describes the graph of h(x) = −3(x − 1)²(x + 1)²(x + 2)? O-12 O -10 -0 -4 -12…

A: see below the answer and explanation

Q: 5] Sketch the graph of r(t) = and shov the direction of increasing t.

A:

Q: Which of the following is a graph of F = (1, 0, 0)? O

A: To find out the correct option.

Q: This graph shows how the number of crates of nails that Ernesto's Construction has left is related…

A:

Q: Draw the graph of f(x) 2* - 1 %3D - 40- 7- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 78 9 10 -2 -3…

A: In this question we have  to draw the graph of the function and  we have given the points on the…

Q: Sketch a graph of y I – 1

A: Given: y=-x-1 To do: Graph the given function.

Q: Draw a rough sketch of the graph f(x)=ax²+bx+c if:a0

A: Explanation of the solution is given below..

Q: The following graph represents x 0<x<T fx) = 0 TくXく2 1.

A: Given graph is

Q: The 3 graphs are for three plants. Piant 1 Plant 2 Plant 3 12 12 12- 11 10- 10- 10 9. 9. 9- 8 8- 7 7…

A: Graphs of three plants;

Q: Find the total length of the graph of the astroid x2/3 + y2/3 = 4

A:

Q: Choose the graph of y = In(x – 2)

A: Basics of Calculus.

Q: On the same set of axes, sketch the graphs of On the same set of axes, sketch the graphs of S(x) =…

A: Sketch the graph on same set of axes

Q: Determine if the graph shown below is Eulerian or Not A) B) C) G, o Eulerian o Not Eulerian o…

A: A connected graph G is said to be Eulerian if and only if degree of every is even .

Q: Which of the following pieces of graph are concave up? i. i. iii. iv. A i. only B ii. and iv. C i.…

A: As we know that, A curve is said to be concave up if it is open in upward direction. From the given…

Q: Find an equation for the graph sketched below 8+ 7- 3- 24 -5-4 -3/-2 -1 1 2 3 4 5 -2 2 -3 -4 -5 -6…

A: Given:   Graph is given.     Point: ( 0 , 4 )

Q: Use the graph of y = Cax to determine C and a. Ay 10- C=I 8- 4- 2- -10-8 -6 -4 10 -2- -4- -6- 10-…

A:

Q: The graph of y+z² = 25 in 3-space

A: We will solve the following.

Q: If C is a positive constant, then the graph of y=f(x)+c is the graph of y=f(x) shifted c units…

A:

Q: Use the graphs of {an} and {bn} to find the indicated sum.

A: Use the graphs of {an} and {bn} to find the indicated sum.

Q: Q1) Use shifting graph to sketch a) y = 1- |V2 – x| b) y = -1+ 5sin (2x)

A:

Q: Consider the following two graphs G1 = {{a, b, c, d, e, f}, {ab, a f, ae, bc, bf, be, cd, cf, df,…

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Q: Which of the following represents the graph whose shown?

A:

Q: Q1) Use shifting graph to sketch a) y = 1-|V2 – x| b) y = -1 + 5sin (2x)

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.