(a) Prove that if æ > 3 and y > 4, then ry > 11. (b) Determine the range of f, if f : D → R, where f(x) = x². I. D = (-2, 2) II. D = [-7, 2| III. D = (-4, 2]|

Q: What is the range of the function f(x) = 23 sin 4z+1 ? A) (0, 0) в [금, 16] C [금, 4] D [2, 0)

A:

Q: Let f(x) be a piecewise function defined by - 6x+ a if x - 3 What should be the values of a and b…

A: Continuity

Q: c) <--- i) Draw y = f(x)\ 1 -3, ii) What is the range of y = |f(x)| ? 4

A: A graph of the function  is given.We have to sketch the graph of the function  and find its range.

Q: Let ƒ be the function given by f(x) = ln (23). What is the domain of f?

A: The answer is given below

Q: If f(x) = x2, what is the ordered pair for x = 7 ? %3D O (7,21) O (7,49) O (7,9) O (7,14)

A:

Q: For what value of x is f ( x ) = 10 ? ( - 1, 6 ) ( 2, 8 ) ( 3, 10 ) ( 5, 16 )

A: We have to select one option which given 10 as the value of f(x) on putting value of x

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f-1(E -…

A:

Q: 4. A function is defined using the formula f (x)=E 2T. Which of the following is the value of f(5)?…

A: Given function is: f(x)=∑jxj=25

Q: Given the functions f) - 3" and g(x) = sin x, determine the range of the combined function y-Ag(x).…

A:

Q: 4(a). Define the zeroth divided difference by f[x,]= f (x; ). Write the expressions for the first…

A: As many questions are given and its various subparts, I will solve only the first. Zeroth divided…

Q: Determine whether the statement " If f(x0, y0) = f(x1, y1), then x0 = x1 and y0 = y1. " ,is true or…

A: Given, the statement “if f(x0, y0) = f(x1, y1), then x0 = x1 and y0 = y1’’. We have to determine…

Q: Which one of these statements in relation to the function f(x)= x+3/x is false?

A: Explanation of the answer is as follows

Q: For a functionf (x, y), we are givenf (100, 20) = 2250, and f. (100, 20) = 8, andf, (100, 20) = 7.…

A: The detailed solution is as follows below:

Q: For what value of x is f ( x ) = 0 ? ( - 2, 0 ) ( 0, 2 ) ( 1, 5 ) ( 3, 6 )

A:

Q: 10) Use the graph of f to determine if f is continuous at x = -3. -5 -4 -3 -2 -1 A) no 2- -1+ -2+ 2…

A:

Q: What is the range of the function g(t)=t^2 - 5 when the domain is defined as the set of integers, t,…

A: Find the range

Q: Let f(x) = x + 3 if x ≥ 5, 8 if x &lt; 5. Find f(12) - f(-12).

A:

Q: 5. Which function has both domain and range of all real numbers? a. y = x2-5 b. y = (x + 2)3 c. y =…

A: To find  the function having domain =R and range =R.

Q: What are intervals of concavity of the function f(x) = -2x + 6x² – 3 ? a. Concave upward on (-1, o0)…

A:

Q: .) What is the range of the function y= x^2 - 6? b.) For the function g(x)= x^2 +3x - 5, what is…

A:

Q: The table contains some input-output pairs for the functions f and g. æ| f(x) | g(x) 2 2 9 6 9 3 9.…

A: To evaluate the given expression with the given table values.

Q: 1) Let f(x) be a function with Domain [-6,-2] and  Range [-10,-4]. Find the domain and range of the…

A: Given that for f(x) Domain [-6,-2] and  Range [-10,-4]

Q: 3) Evaluate the function for the given value of x. - 10, if xs6 a) h(1) c) h(-10) h(x) = (-x – 1,…

A: It direct putting value of x type question. Just we need to identify the correct piece

Q: (b) Determine the range of f, if f :D → R, where f (x) = x?. I. D = (-2, 2) II. D = [-7, 2] III. D =…

A:

Q: Suppose that f(x) is a function with f(5) = - 8 and f(9) = 8. Determine which choice best describes…

A:

Q: Let  f(x) = 2 + x + x2 and h ≠ 0. how do i find: f(x + h)

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.