The graph of f (x) = x² was transformed to create the graph of g (x) = f (x + 7). Which statement about the graphs is true? The vertex of the graph of g is 7 A units to the right of the graph of f. C The vertex of the graph of g is 7 units to the left of the graph of f. The y-intercept of the graph of g is 7 units below the y-intercept of the graph of f. The y-intercept of the graph of g is 7 units above the y-intercept of the graph of f.

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

A:

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: how is the graph g(x)=(x-6)^2-4 related to the graph of f(x)=x^2?

A: In this question transfomation takes place.

Q: The graph of y = 5(x) is obtained by a/an stretch of the graph of y = f(x) by multiplying each of…

A: Given graph is y=f(x).

Q: How is the graph of g(x) = (x - 8) 2 + 7 transformed from the graph of f(x)=x2?

A: g(x) = (x - 8)2 + 7 f(x) = x2 is the parent function. The function g(x) can be obtained by applying…

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

A: Given

Q: h(x)=8x3+8x2−3x−2, what is the x coordinate of the inflection point for the graph of h(x)? (Do not…

A:

Q: How Is the graph of g (x)=x2+14 related to the graph of f(x)=x2? The graph of g (x)=x²+14Is the…

A:

Q: neath the graph of f(x) = 7x³ about the y-axis ov

A:

Q: Graph g(x) and –g() -9() from g(x)? on the same axes for the x-interval x E [0, 5]. How did you get

A: we have to get the graph -g((5-x)/2) from g(x)

Q: Suppose that f(x) = x2 + 4x - 21.(a) What is the vertex of f?(b) What are the x-intercepts of the…

A: a. The vertex parabola lies at x=-b2a for the f(x) =ax2+bx+c vertex is at x…

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: How is the graph of g(x)=(x-3) related to the graph of f(x) = x?

A:

Q: How does the graph of f(x) 22 compare to the graph of g(x)= 2"+27 whereas the graph The graph of…

A:

Q: The graph of f(x) = x² is shifted 3 units to the left. This graph is then vertically shrunk by a…

A: Given: f(x)=x2 shifted 3 units left vertically shrunk=15along x-axis shifted downwards by7 units

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: For f(x) = −x2 + 8x − 4, the value of −b/2a is 4. Find the y-coordinate of the vertex of the graph…

A: Definition used:The vertex of a graph is the maximum or minimum point of a parabola.The x value of…

Q: The function f(x) = 3 - 4x - 2x2 is shown on this graph. f(x) 6 + 2 그 What value of at corresponds…

A:

Q: Suppose that the x-intercepts of the graph of y = f(x) are -3 and 7.  (a) What are the x-intercepts…

A:

Q: How is the graph of g(x)=f(kx) related to the graph of f when k = 5?

A:

Q: How does the graph of f(x) = 2*+2 compare to the graph of g(x) = 2* + 2? The graph of f(x) is a…

A: The graph f(x) is a translation of the parent function h(x) =2x 2 units to the left Given functions…

Q: Which is the graph of f (x) 2x + 8x ? = -x Which is the graph of h (x) = 2(x + 1)(x´ - 9) - 2(+ +…

A: Given, fx = -x4 -2x3 +8x2  hx = 2x+1x2 -9  we have to choose the graph of fx  and  hx

Q: How does the graph of f(x)=(x-9)'-3 Compare to the parent function gx) = x". |

A: Given, f(x)=(x-9)4-3 g(x)=x4

Q: The graph of f(x) = x2 – 7 is horizontally stretched by a factor of 4.5. Write the equation…

A: Here the graph of f(x)=x²-7 is horizontally stretched by a factor of 4.5.  We want to write the…

Q: Suppose that f(x) = x2 + 2x - 8.(a) What is the vertex of f?(b) What are the x-intercepts of the…

A: (a) Given function is: fx=x2+2x-8 Let y = f(x) Then we get,…

Q: Suppose that the​ x-intercepts of the graph of y=​f(x) are −7 and −4.

A:

Q: c. If A(x) = x² In(f(x)), what is the value of A'(2)? What does this result say about the behavior…

A:

Q: (a) How is the graph of y = f(x – 3) + 2 obtained from the graph of f? (b) How is the graph of y =…

A: Let the given graph is f(x). (a) To obtain the graph of y=f(x-3)+2 First, horizontally translate the…

Q: The graph of 5% = where x > 0, lies entirely to the right of the y-axis O below the x-axis above the…

A: Given: Graph of the above is,

Q: For f(x) = −x2 + 8x − 2, the value of −b/2a is 4. Find the y-coordinate of the vertex of the graph…

A: Solve the following

Q: How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3?

A: Givenf(x)=(x+1)3-8 g(x)=x3here,g(x) is the parent function and f(x) is its transformed function

Q: 6) Consider the function f (x) = x² + 2x – 48 find the coordinate of the vertex, the y-intercept,…

A: Given: Quadratic function, f(x)=x2+2x-48

Q: The graph of y=f(x)= ^3 √x -9 is horizontally stretched away from the y-axis by a factor of 3 to…

A: Given: y=f(x)=x3-9 To determine: Equation of new function when the graph is horizontally stretched…

Q: Use the graph of g to solve: For what value of x is  g(x) = 1?

A: The graph of function is given.

Q: The graph of f(x)=x^2 was transformed to create the graph of g(x)=f(x)-9. Which statement about the…

A: I have provided solution in step 2.

Q: Use the graph of g to solve: Find g(2)

A: Given graph is: To find: g2 From the given graph we can find that at x=2, value of function is -2.…

Q: True or false: The graph of g(x) = √(x + 4) is the graph of f(x) = √x shifted horizontally to the…

A: we have to tell whether the given statement is true or false. Statement : The graph of g(x) = √(x +…

Q: how can the graph of f(x)=1/(x-9)^2 + 7 be obtained from the graph of y= 1/x^2 ?

A:

Q: F

A:

Q: The graph of y= f(x-3) is the graph of y= f(x) 4 A. vertically compressed by a factor of 4 and…

A: Given function y=14f(x-3) with parent function y=f(x).

Q: Find the vertex of the graph. f(x) = −x2 + 6x + 1

A:

Q: For f(x) = −x2 + 8x − 8, the value of −  b 2a  is 4. Find the y-coordinate of the vertex of the…

A: The equation f(x)=-x2+8x-8 represents a parabola.  This can be visualized from the graph. The…

Q: Find the x- and y-intercepts of the graph of the function f(x)=−2|x+5|+2. Enter your answers as…

A:

Q: To obtain the graph of f(x) = (x – 3)3 +7, shift the graph of y = x³ to the right units and up…

A:

Q: Consider the graphs of y1 = f(x) and y2 = f(2x + 7). Make a prediction about how these graphs are…

A:

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: Suppose (1, 3) is a point on the graph of y = f(x).• What point is on the graph of y = f(x + 3) −…

A: y = f(x + 3) − 5 means y=f(x) moved 3 units left and 5 units down. (x,y) -> (x-3 , y-5). So,…

Q: suppose that the x-intercepts of the graph of y=f(x) are: -7 and 2  what are the x-intercepts of the…

A: The x intercepts of the graph, y is given below.

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.