Assume that we know that f(x) is a one-to-one function. a. If f(-1) = -8 then f-1(-8) = b. If f-1 (9) = 5 then f(5) = c. If (13, –23) is a point on the graph of y = f(x), - then f( )=| and f( )=|

Q: (x-4)(x-3) Determine the points of discontinuity for the function f(x): = (x-3)(x+2) a. (3.- 1/3) 5…

A: To determine the points of discontinuity for the function f(x)=(x−3)(x+2)(x−4)(x−3)​ , we need to…

Q: Which of the following is a point on the graph of the function 5 - 3x f(x) = 4. (-5, 5) (2,-1) (1.4)…

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Q: what is the equation of the following linear unction f(x) through the points (-5, -2 and (7,-3)

A:

Q: Which of the following relations is not a function? a.{(3,3), (2,3),(0,4),(1,4)} b. {(3,3), (2,3),…

A:

Q: Describe the end behavior of the function f (æ) = -2x+ 3x2 – 5a + 1. f (x) as x → ,f (x)→ as x →

A: We have to describe the end behavior of the function f(x)=-2x4+3x2-5x+1.

Q: Let H(t) be the height of snow in inches as a function of time (in hours) after midnight. How wa…

A:

Q: A bucket has a leak that started 6 hours ago. At time 0, when the bucket just emptied, a tap was…

A: Which option represents  the amount of water in the second bucket.

Q: What is the vertex of the following function? f(x) = x² + 4x +3 (-1,4) (-2,-1) (4,3) (-4, 3)

A: Solution : Given that f(x) = x^2 + 4x + 3 For vertex of the given function , f'(x) = 0

Q: Graph the function. f(x) = 4x - 1 y y 10 10 5 5 -10 -5 TO -10 -5 5 10 -5 -5 –10 -10 y y 10 10- 5 5…

A:

Q: A 1.Find the domain of following functions: a.f (x) = {(2,6), (3, 9), (7, 11), (4, 0), (-1, 12)} and…

A: We are asked to find  domain and composite of the function

Q: Assume g is a one-to-one function. If g(x) =x2+ 10x with x 2 -5, find g1 (4) 2. 10+ 10 а. b. -10 -6…

A: Consider the function,

Q: The following represents the graph of a function f(x): 3 1 2 3 -1 -2- On a separate set of axes,…

A:

Q: Refer to the functions f and g and evaluate the functions at x =-2. f = {(2, -1), (1, 1), (-4, -6),…

A: (f+g)(-2)=f(-2)+g(-2)  Substitute   f(-2)=-8  ,    g(-2)=-5in the above equation

Q: Which of the following functions has a graph with a vertex that is a translation 5 units…

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Q: If (1, a), (b, ), (c, 17) are points on the graph of the function h(t), which points are on the…

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Q: The function S (2) = x over the domain (0, 00) is shown. 10

A: Inverse function is find by switching x into y and y into x , then solve for y .

Q: A function is defined as f (x) = 8x +15. The values of the domain are[1,3,4,6) what are the values…

A: Given,            f(x) = 8x + 15

Q: For the given function f(x)=x²-32x + 32, determine an appropriate viewing rectangle. O [-10, 40] x…

A:

Q: If (-1,8) is a point on the graph of y = f(x), which of the following must be on the graph of y…

A: We have to find the point which must be on the graph of y= f(-x).

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.