1. Find the domain and the range of each of the following functions. (a) Vr - y2, (b) e2+y + 1.

Q: This function has: 1) A y intercept at the point 2) x intercepts at the point(s)

A: Given,  fx=2x2+11x+123x2+10x+3 The x-intercept, y-intercept, and vertical asymptotes are to be…

Q: The domain of the function ,y) = In[x* +y² – 1) is:?

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Q: nd the points where the function f(x) = (x² – 1)³ is decreasing, -

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Q: Find the formula for a function of the form y=be^((-(x-a)^2)/2) with its maximum at the point (0,5).…

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Q: (b) Determine the domains and range of this function: y = v1 -x-

A: The given function is y=1-x2 the domain of the function is -1≤x≤1 In the interval notation the…

Q: -Which of the functions below has a range of y<-2?

A: Idea: Construct the line y = -2. If the graph remains below the line y = -2 then the function have…

Q: 2 The function f(x) is linear and it decreases for all values of x. On the coordinate plane, draw a…

A: We want to find a decreasing linear function.

Q: If the critical point of the function f(x.y)-x- y- 2xy +6 is (0.0). test this point whether it is:

A: We use second order partial derivative to know about critical point behaviour

Q: Suppose that f(x) is a linear function. So, the algebraic representation of f(x) is of the form:…

A: The algebraic representation of the linear function is fx=mx+b

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in…

A:

Q: B. Find and classify the extreme points of function f(x, y) x* +y-4xy-1.

A: Maxima minima of two variables function

Q: Suppose that f is a linear function with slope -3.6 and that f (1) = 4. What value of x gives f(x) =…

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Q: Suppose that f is a linear function with slope -3.6 and that f (2) = 8. What value of x gives f(x) =…

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Q: Let P=(x,y) be a point on the graph of y=x2-5  a) Express the distance d from P to the origin as a…

A: P=(x,y) be a point on the graph of y=x2-5

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Given graph is as follows where the red graph shows f(x)  and a line tangent to the curve at x=4.…

Q: -2 if x 2

A: Given function is : fx=-2 , if x≤0x2 , if 0&lt;x&lt;2-x , if x≥2 To draw the graph .

Q: Describe how you could use the graph of f(x) = 2" to obtain a decimal approximation for V2.

A: y=2x

Q: 9. Determine the coordinates of a point(s) that do not change between the original and the…

A: Given that: f(x)=-x2+5

Q: -3. 3) to the curve given by f(x) =

A:

Q: Find the net change in the value of the function between the given inputs. f(x) = 3x - 2; from 1 to…

A: f(x)=3x-2now we have to find the net change in the value of function from 1 to…

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: Given that

Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   =&gt; the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: Graph the functions in excercise

A: Given function, y=x-13-1

Q: /hich of the following best describes the end behavior of a function with an odd degree and negative…

A: We have, Odd degree with negative leading coefficient.

Q: Find the net change in the value of the function between the given inputs. f(x) = 4 - 5x; from 3 to…

A: To find net change in the value of function: f(x)=4-5x;from 3 to 5. Solution:…

Q: Match f(x) with its graph without using a calculator. -… (x)

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Q: Find the global extrema of the function f(x)=e−x2.

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Q: 16. Find the range of the function y = 1+ x2

A: Range: The range of the function is the set of all values of the dependent variable y corresponding…

Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

A:

Q: does y=e9-x2-2 exist? whaet is the domain and range of the function if exists

A: Consider  y=e9−x2−2

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: f(x) = is the range in which the function is decreasing.

A: fx=exx Differentiating with respect to x, we get f'x=dexdx·x-dxdx·exx2…

Q: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

Q: 1. Make two separate plots of the function f(x)=0.6x-5x +9x+2; one plot for -4 sxS4, and one for…

A: The given function is fx=0.6x5-5x3+9x+2.

Q: 4. Identify and sketch the graph of three distinct level curves of the function. f(x, y) = Ln(y –…

A: Given that the function fx, y=lny-3x. We have to sketch the graph of three distinct level curves of…

Q: 6. a. Use an x- interval of 0.0001 to determine the instantaneous range of change of the function…

A: Consider the given function. fx=x4+8x3+19x2+12x The objective of the problem is to find the…

Q: Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

A:

Q: A researcher believes that if x thousand individuals among a susceptible population are inoculated…

A: Given: I(x)=aRx-b R=0.9

Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

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Q: The interval in which the given function is decreasing is at 3 points y = x3 – x2 – 5x - 4 (-00, -1)…

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Q: - Find the domain of the following functions: a- y=2x. y = (x+1) c-y = - Vx+4 (3-х)

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Q: Find an equation of the line tangent to the graph of f(x) at the point (5,9): f(x) = e-3x-1o + 8

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Q: Find the net change in the value of the function between the given inputs. f(x) = 4-5x; from 3 to 5

A: We want to calculate net change in given function from 3 to 5.

Q: Find the level curve of the function at c=2 for g(x,y)=(x^3-y)

A: A scalar function g(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Suppose that f is a linear function with slope 2.4 and that f(5) = -1. What value of x gives f(x) =…

A: Consider a linear function f with slope 2.4 and f(5)=-1 .

Q: QUESTION 2 Differentiate of the following function with respect to x. a) y = x³ln (2x) 3x2+10 b) y =…

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Q: Find the maximum or minimum value of the function. f(s) = s2 - 1.2s + 16

A: f(s)=s2-1.2s+16Formula for the equation isf(x)=ax2+bx+cx=-b2aSo, s=-(-1.2)2  =0.6

Q: 19. Find the absolute extrema of the function on the indicated interval. f (x) = xe-3x;[-1,2] хе

A: As a first step, we need to find all the critical points by equating the derivative of f(x) to zero.…