The function f is defined as follows. f (x) = - 2x²+ 4 If the graph of f is translated vertically downward by 5 units, it becomes the graph of a function g. Find the expression for g (x).

Q: Suppose the graph of the function f(x) looks like -1 Of the following graphs, which is the graph of…

A: The most easiest way to draw f-1(x) is to draw mirror image of the graph of f(x) across the line…

Q: (4) Draw the graph of the function f(x) = 2¹. (5) Draw the graph of the function f(x) = 3.

A: Consider the functions 4)     f(x)=2x5)     f(x)=3x

Q: The range of the function f(x) = 3/25 – x² + 2 is

A:

Q: Suppose that f(x) = 3x . (a) What is f(4)? What point is on the graph of f ?(b) If f(x) = 1/9, what…

A: GIVEN f(x) = 3x . we need to find the  (a) What is f(4)? What point is on the graph of f ?(b) If…

Q: Suppose that f (x) = 2x . (a) What is f(4)? What point is on the graph of f?(b) If f(x) = 1/16, what…

A: The given function is fx=2x

Q: The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7 resembles the graph of ________ for large…

A: The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7resembles the graph of ________ for large…

Q: Find the slope of the graph of the function at the given point.

A:

Q: Find the domain and sketch the graph of the function.   f(x) = |2x+1 |

A: The given modulus function is well defined for all real numbers. Therefore, The domain of given…

Q: Consider the graph of the function f(x)=(x^2−4 )/ (x^2−12x+20.) Find the x-value of the removable…

A: The function f(x) will have a removal discontinuity at x = a when the function will have a finite…

Q: 6 Select the correct graph of the function f(x)= x+4:

A:

Q: find the points of inflection and discuss theconcavity of the graph of the function. f(x)=-x^{3}+6…

A: Given: The function fx=-x3+6x2-5, To determine: The point of inflection and concavity of the graph…

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: Sketch the graph of the function given. (a) f(x) = 4x - x2     (b) g(x) = |4x - x2 |

A: Given: f(x)=4x-x2 g(x)=|4x-x2|

Q: Graph the function defined by g(x) = |x + 2|.

A: Given function is, gx=x+2. Graph the absolute value using the vertex and few selected points.   x…

Q: Find the domain of the function : g(x) = √(x-3) + √(x+4)

A:

Q: 6. Use the graph of f(x) - to write an equation for the function whose graph is shown.

A: Given data: The given graph of the polynomial. The first point on the graph is (-2,0). The second…

Q: If f(x) = ax3 + bx2, determine a and b so that the graph of f will have a point of inflection at…

A: Topic = Application of Derivative

Q: The graph of f (x) = x² is horizontally stretched by a factor of 4, and then shifted to the left 2…

A: Solve the given problem.

Q: Find the points of inflection and discuss the concavity of the graph of the function. g(x) = x√(x +…

A:

Q: graph the function:f(x)=-2 for x

A: Graph the function: f(x)=-2 for x

Q: The graph of f(x)=3x is reflected about the y-axis and stretched vertically by a factor of 4 . What…

A: Given,         The graph of f(x)=3x is reflected about the y-axis and stretched vertically by a…

Q: What values of x would be found in the in the domain of function f(x)=10/x-2

A:

Q: The graph of f (x) = x² is horizontally stretched by a factor of 2, and then shifted to the left 4…

A: Given, fx=x2

Q: determine where the graph of the function is concave upward and where it is concave downward. g(x)=…

A:

Q: Graph the function by using its properties.   f(x) = x2 − 4x + 3

A: First we find the domain, axis of intercepts, vertex and range of the function. By using this we…

Q: Find the domain and sketch the graph of the function   g(x) = |x| -x

A: Given: gx=x-x first we simplify given function if, x≥0 then x=x and if, x<0 then x=-x so,…

Q: Find the domain and sketch the graph of the function.   f(x) = x2 - 2x + 1

A: Let us consider the given function. Since, the functionis a polynomial, so the domain is all real…

Q: If f (x) =ax³+ bx² , determine a & b so that the graph of f will have a point of inflection at (1,2)

A:

Q: Find the domain of the function g(x) = 1/∣x2 − 4∣

A: Consider the function: gx=1x2-4

Q: Given the function f(x) whose graph is shown below, determine f(0). f(x) -6 -5 -3 -2 -1 -1 Provide…

A:

Q: Find the domain and sketch the graph of the function. f(x) =2t+t2

A: Given: fx=2x+x2 we know that given function is a quadratic function whose constant term is zero we…

Q: The functions f(x) = 3-x and g(x) = -3x have the same graph.Determine whether the statement is true…

A: Consider the given function fx=3-x and gx=-3x

Q: Graph F(x) = -(x + 1)(x – 1)^2(x – 2) by doing the following. Plot all the points where the graph…

A:

Q: Find the domain and range of the function. g(x) = √6x

A: The given function is gx=6x. Find non-negative values for radicals:  6x≥0x≥0 The domain of the…

Q: For the function f(x) whose graph is shown, what is the value of f(4)?

A:

Q: Determine where the graph of the function is concave upward and concave downward and find all…

A:

Q: Consider the graph of the functions f(x)=(x−5)² and g(x)=−3x+13. What are the points at which…

A:

Q: Find the point of the graph of the function that is closest to the given point: f(x) = 2x+9 ;…

A:

Q: Find the range of values x for which the function f(x) = 4x³ – 12x2 + 15 is decreasing. a)

A: To find the range of values of x for which f(x) is decreasing

Q: Find the domain of the function. 8 f(x) =- X-14

A: Our Aim is to find domain of f(x)=8/(x-14).

Q: If f(x) = ax3 + bx2, determine a and b so that the graph of f will have a point of inflection at…

A: Given f(x) = ax3 + bx2

Q: If f and g are the functions whose graphs are shown, and h(2) = f(x)g(x), find h' (2). 6 -2. -2 2.

A:

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

A: The graph of the function is

Q: Find the point on the graph of the function that is closest to the given point: f(x)= 2x+8; (0,18)

A: We have given f(x)= 2x+8; (0,18)

Q: Find the domain of the function. g(x) = 5x+5 What is the domain of g?

A: The given function is gx=5x+5To find its domain

Q: Find the domain of the function g(x) = (x - 6)/(x2 - 36).

A: We have to find the domain of the function g(x)=x-6x2-36.

Q: Find the domain of the function : h(x) = √(8 - 2x)

A: Domain is the range of values of x for which the function is defined.Given function - h(x) = 8-2xFor…

Q: The graph of f(x)=x^2 rises or falls to the left? And does it rise or fall to the right?

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.