. The graph of y= h(x) is shown below. The function f(x) is defined by f(x)=--h(x)+3. (a) What three transformations have occurred to the graph of h to produce the graph of f? Specify the transformations and the order they occurred in. (b) Graph and label the function f(x) on the grid below that contains h(x).

Q: Draw the graph of f(x) = mm. 6+3 10+ STAT ~~ 10-9-8-7-6-5 -4 -3 -2 -11 SE -9 0 4 5 6 7 8 9 10

A:

Q: 52. Let if x 2 | (b) Sketch the graph of g.

A: Domain of g(x) is divided into parts.We have to draw different path for different part of domain.…

Q: The graph of the function f(x) = /x Is stretched vertically by a factor of a and is translated3…

A: Shifting or transformation of graph is very useful. When a graph is shifted or stretched or…

Q: Compute all the vertical asymptotes of the function x2 + 1 y = Зх— 2х2 Produce the graph of the…

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of the…

Q: 14. Identify the graph of the function below: f (x) = 2* – 3 -3 -1 -8 -7 -6 -5 -4 -3 -2 -1 1 2 -1 1…

A: satisfy function value at some point

Q: Draw the graph of f(x) and discuss its differentiability at x = 1.

A: Given fx=x2,     x≤1x,   x>1

Q: he graph of y=x^2 is expanded vertically by a factor of 2, translated 5 units to the left, and…

A: Given function y=f(x)=x2

Q: 4. Use transformations of y= x* or y=x to graph cach function. (a) S(x)=(x+3)' (b) f (x) = (x-1)* -…

A: a)y=x5Horizontal shift by 3 units towards leftf(x)=(x+3)5 The graph is shown below:

Q: 16. Use transformations to sketch the graph of f(x)= vx- 3+2.

A:

Q: 4. The graph of the function f(x)= /16-x² is a half-circle. If we shift this graph 2 units to the…

A:

Q: Below is the graph of y=x. Transform it to make it the graph of y= -2(x-4)°. 中

A:

Q: 7. Sketch a graph of the function c(x) = (½x)³ – 1. Describe the transformations to the graph of y =…

A: Given query is to find the graph of the function and provide transformation used.

Q: 1. Find x- and y- intercepts of the graph of f, if it has any.

A: Note: As you have posted the multiple numbers of questions, so we are going to solve the 1st…

Q: The graph of y = f(x) is graphed below. What is the end behavior of f(x)? %3D 60000 50000 40000…

A: We can easily read the end behaviour of the graph by just looking the x values and their…

Q: 4. Sketch the graph of f(x) = and give its domain, intercepts, and %3D +2x-3 asymptotes.

A:

Q: 8. Given (x) - x', sketch the graphs from y = f(x) to 1 1 (x + 6) 2 (x - 5 = -

A:

Q: Below is the graph of y=x. Transform it to make it the graph of y=-x-4-2.

A: a) y=-x-4-2b) y=-2x-4

Q: 8)If f(x)=x/(x-1)^2, f(x)=(x+1)/(x-1)^3 f"(x)=(2x+4)/(x-1)^4 Graph this function using all available…

A: Given function is: fx=xx-12 A function is sad to be undefined at a point where its denominator…

Q: 6. Determine the domain and range of the graph of the transformed function shown. * 2

A:

Q: Describe a sequence of transformations that can be used to obtain the graph of y = 1+e2-1 from the…

A: Given: y=1+e2x-1

Q: {2*+1 if x<0 etch the graph of f(x)=X+3 EO

A: We will graph the problem.

Q: (1+ 3x X 1

A:

Q: Find the inverse of ƒ(x) = x + b (b constant). How is the graph of ƒ -1 related to the graph of ƒ?

A: To find the inverse we plug f(x)=y Then switch x and y and solve for y

Q: Suppose that the graph of a function f is known. Then thegraph of y = f(x - 2) may be obtained by…

A: Consider a function y=fx Then if the graph of function y=fx is shifted horizontally towards right by…

Q: The graph of f(x) is given on the grid. Graph f'(x), its derivative. 05 4 -8 -7/-6 -5 -4 -3 -2 -1 I…

A:

Q: Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes…

A: Given,

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: How can the graph of f(x) = 1 + 15 be obtained from the graph of y =,? x-5 X- 5 O A. By making a…

A: Solve the following

Q: The graph of f (r) -x² was transformed to create g (x) = from the graph of f to the graph of g -(x +…

A: Here f(x) = - x2  And g(x) = - ( x + 3 )2

Q: Below is the graph of y=x". Transform it to make it the graph of y=-3(x-2).

A:

Q: Explain how the graph of g is obtained from the graph of f. (a) f(x) = x, g(x) = (x - 5)3 O shift…

A:

Q: 9 Draw a graph of y = f(x) such that f(-2) = 5, f(1) = 0, and f(4) = 3. %3|

A: Given:

Q: The cumulative number of cases of AIDS(acquired immunodeficiency syndrome) in the United States…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 0. if a 2

A:

Q: Use the graph of y = f(x) to sketch the graph of f'(x). 10+ 9. 8+ 7+ 6+ 5- 4+ 10 -9 -8 -7 -6 -5 -4…

A: The point of inflection for the graph is obtained as .

Q: sketch the graph of the function = 2-4cos x

A:

Q: If f(x) = 4x2 – x³, find f'(x), f"(x), f'(x), and f(4)(x). f'(x) = f"(x) = f""(x) = f(4) (x) = Graph…

A: Given, the function f(x) = 4x2 – x3, then we have to find the f’(x), f’’(x), f’’’(x) and f4(x) and…

Q: Consider the function: y=3|x+2|−1 What is the base graph and what are the transformations for this…

A: Consider the given function y=3x+2-1

Q: 1. Sketch the graphs of the following functions: N(a) y=x² y= 3x2 y = 4x y =-3x ² y=-4x2 y=ー ー=へ)…

A: Since you have posted question with multiple subparts , we will solve the first three subparts for…

Q: Use the guidelines of the section to make a complete graph of ƒ.

A: The given function is f(x) = 1e-x-1

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: Previous Sketch a graph of f(x) - (r + 1)* + 2 5- 4 3 2 -6 -5-4 -3 -2 -1 -1 | 2 3 4 5 -2 -3 -4 Clear…

A:

Q: A reflection in the x-axis of the graph of y = f(x) is represented by h(x) = ________, while a…

A: Since, we know that the reflection of point (a,b) in x-axis is (a,-b)and the reflection of point…

Q: Below is the graph of y: Transform it to make the graph of y =- X-1 %23

A: The parent function is the simplest form of the type of function given. y=1/x   For a…

Q: What is the new equation for the pictured graph after transformations from the parent function…

A:

Q: Question 2: Identify the co-ordinates of any local and absolute extreme points and inflection points…

A: Given: y=4x3+21x2+36x-20y'=12x2+42x+36=0⇒2x2+7x+6=0⇒x=-2   or  x=-32

Q: 10. Use the function f(x) = (-2)e +1 to state the transformations and then graph: a= h= k= y

A: In the question we have to find values of a , h , k and graph the given function.

Q: 4) Sketch the graph of the derivatives f' of the given graph below on the same grid.

A: The derivative of a function at a point is the value of the slope of the tangent to the function at…

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.