f(x)+a : shift upward a units
f(x)-a : shift downward a units
f(x+a) : shift left a units
f(x-a) : shift right a units
-f(x) : reflection across the x-axis
f(-x) : mirror; reflection across the y-axis
To determine the resulting function after applying a sequence of transformations to ( f(x) = x^5 ), you need to specify the transformations applied (e.g., shifts, stretches, reflections). For example, if you apply a vertical shift upwards by 2 units, the new function would be ( f(x) = x^5 + 2 ). If you reflect it over the x-axis, it would become ( f(x) = -x^5 ). Without specific transformations, the resulting function cannot be definitively identified.
To determine the resulting function after applying a sequence of transformations to ( f(x) = x^5 ), we need to specify the transformations. Common transformations include vertical shifts, horizontal shifts, reflections, and stretches/compressions. For example, if we apply a vertical shift up by 2 units, the resulting function would be ( f(x) = x^5 + 2 ). Without specific transformations, we can't define the exact resulting function.
The local extrema of f(x) = x + 2*sin(x) are 6.2832 and 2.4567 (approx).If the question was about some other function of x, please resubmit using words for mathematical symbols. The browser that you are required to use for posting questions is rubbish and will reject most mathematical symbols. In this case, all that I can see is "f(x)x 2sinx" and have had to guess the rest.
The identity function is a mathematical function that always returns the same value as its input. In formal terms, for any input ( x ), the identity function is defined as ( f(x) = x ). It serves as a fundamental concept in various fields, including algebra and calculus, and is used to illustrate the properties of functions and transformations. Essentially, it acts as a "do nothing" function, leaving its input unchanged.
To determine the vertex and transformations of a given function, we first need the specific function itself. For example, if the function is in the form (f(x) = a(x-h)^2 + k), the vertex is ((h, k)). The transformations from the parent function (f(x) = x^2) would include a vertical stretch/compression by factor (a), a horizontal shift (h) units, and a vertical shift (k) units. If you provide the specific function, I can give a more detailed answer.
Nope.* * * * *The above answer is so wrong!Suppose f and g are two transformations wheref(x) = 2x, andg(x) = x2Then f(g(x)) = f(x2) = 2x2Whileg(f(x)) = g(2x) = (2x)2=4x2Therefore f(g(x)) = g(f(x)) only when x = 0
The function f(x) is important in mathematical analysis because it represents a relationship between an input x and an output f(x), allowing for the study and understanding of various mathematical concepts such as continuity, differentiability, and integration. It helps in analyzing and solving complex problems in calculus, algebra, and other branches of mathematics.
+, -, x, ÷ for addition, subtraction, multiplication and division respectively.
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
The browser used by this site for posting questions is almost totally useless for many mathematical questions because it rejects most mathematical symbols and does recognise superscripts.I am assuming the expression is f(x) = 900*(0.65)^x. If so, the domain is x>= 0.
To calculate f times x, you simply multiply the value of f by the value of x. This can be represented as f * x. For example, if f = 5 and x = 10, then f times x would be 5 * 10 = 50. Multiplication is a basic arithmetic operation that involves repeated addition and is essential in various mathematical calculations.
The browser used by this site for posting questions is almost totally useless for many mathematical questions because it rejects most mathematical symbols and does recognise superscripts.I am assuming the expression is f(x) = 900*(0.65)^x. If so, the domain is x>= 0.
It is difficult to be sure because the browser used for posting questions on this site is utter rubbish and strips out all mathematical symbols. If your question was f(x) = x + 2 then the inverse is f(x) = x - 2.
The local extrema of f(x) = x + 2*sin(x) are 6.2832 and 2.4567 (approx).If the question was about some other function of x, please resubmit using words for mathematical symbols. The browser that you are required to use for posting questions is rubbish and will reject most mathematical symbols. In this case, all that I can see is "f(x)x 2sinx" and have had to guess the rest.
f(x) = Cos(x) f'(x) = -Sin(x) Conversely f(x) = Sin(x) f'(x) = Cos(x) NB Note the change of signs.
F = 32 + C x 1.8 or C = (F - 32) x 5/9 Where F is Fahrenheit and C is Celsius.
The identity function is a mathematical function that always returns the same value as its input. In formal terms, for any input ( x ), the identity function is defined as ( f(x) = x ). It serves as a fundamental concept in various fields, including algebra and calculus, and is used to illustrate the properties of functions and transformations. Essentially, it acts as a "do nothing" function, leaving its input unchanged.