Q3:- Šketch the following functions showing the detailed steps in different graphs: c) f(x) = 1 – (x – 2)²

Q: Find the point "P" on the graph of the function y=sqrtx closest to the point (10,0)  The x…

A: Let the point is (x,y)= (x,sqrt(x))Distance of (x,sqrt(x)) from (0,0) is D

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

A:

Q: Find the inflection point of the curve f(x)=2x³ – 18x²+ 30x. О а.3 O b. 3/2 С. 9 O d. None

A: We have to find out point of inflection

Q: For the following function, y = -32 + 15x + 6x² – x³ (a) find the critical values, (b) test for…

A: Given:     y=-32+15x+6x2-x3 We have to find: Critical values, and test for concavity to determine…

Q: Find the domain of function defined as follows. y = ln(x2 - 16)

A: y=lnx2-16Domain:       The domain of a function is the set of all possibleinputs for the function

Q: Plot the function f(1) for -10 <xs 10. %3D 1+e5.5 – 1.5x 20

A: Graph of any function can be plotted by joining the points from which the function passes. So to…

Q: Find the point P on the graph of the function y=sqrtx closest to the point (9,0) The x coordinate of…

A: We have to find the point P on the graph of the function y=x closest to the point (9,0). Also, find…

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: Sketch the curve of f 3x y = f(x) = r³ – 8

A: Given,  y = fx = 3xx3-8  We have to sketch the curve.

Q: Determine the range of the following functions. Express your answers using interval notation y =…

A: The graph of y=3x2, -2≤x≤2 is shown below:

Q: Q3): Does the function r(x, y) = xs -xay² is harmonic?

A: As we know that; the function fx,y is harmonic. If ∂2f∂x2+∂2f∂y2=0 or fxx+fyy=0 Given:…

Q: Juanita wishes to have a rectangular garden in her backyard with an area of 64 ft2. Letting x denote…

A: we know that area of rectangle =  length × width

Q: How do you use the graph of f(x) shown to the right to find the following, if they exist. If a…

A:

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: with the approphe Choose the correct function below. OA. O B. Oc. z=3-(2 -4)²• (2 -1)?

A:

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent. (x, y) = Need…

A:

Q: with equation -x+3, x -1 f(x) = %3D What is the behavior of f(x) as x gets closer and closer to -1…

A:

Q: What is meant by “the value of a function at x”?

A: Let the function be f(x).

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

A:

Q: - Plot the function y=(3cos(x)-sin(x))*e®* -0.2x for -45x9 with increment-D0.1

A: Here, the given function is  y=(3 cos(x) -sin(x))e-0.2x for the interval -4≤x≤9 with increment…

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

A:

Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: 7. Determine the equation of the function with zeros at ±1 and - 2, and a y-intercept of-6. Then…

A: We have to find function

Q: the y intercept of a function f(x) is (0,b). What is the y-intercept of f(x) +k ?

A: Given that the y intercept of a function f(x) is (0,b).f(x)+k means k units higher than f(x). So the…

Q: 1. f() 3 2х + 3

A:

Q: Explain why the graph of f(x) = 2a+1 has no horizontal tangents.

A: Solution :   In the given question we have to find why the graph of given equation has no horizontal…

Q: Find the point on the graph of the function that is closest to the given point. f(x) = /x, (3, 0)…

A: Given, y = f(x) = x Let's assume the closest point to (3,0) will be (x, y) then (x,y) = (x, x)…

Q: What is the equation of the function that is obtained from f (x) = ⎷x by shifting 1 unit to the…

A: If we shift f(x)= sqrt(x) 1 unit to right then we get f(x)=sqrt(x-1)

Q: Find the point on the graph of the function f(x) = (x + 5)² that is closest to the point (1,3). %3D…

A: It is given that, f(x)=x+52 that is closest to the point 1,3.We have to find the point on the graph.…

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: For what value(s) of x does the graph of f(x) = 4x3 - 6x2 - 144x - 24, have a horizontal tangent?

A:

Q: Find the fx(x, y) and fy(x,y) of the following function x² – y3 f(x,y) %3D Inxy

A: Given: fx,y=x2-y3lnxy

Q: What is the equation of the function that is obtained from f (x) = | x | by reflecting about the x…

A: Given information:The given function is

Q: Consider the function f(x)=x^2+2x+2  what is the equation of the line of symmetry of f?

A: To find equation of line of symmetry of function fx=x2+2x+2

Q: For what x-value is the function y = |x+5| not differentiable?

A:

Q: Starting with the graph of f(x) = 6ª, write the formula for the function that results |3D from (a)…

A:

Q: 8. 4 2

A: In this question we will use basic of calculus i.e use of tangent function. We will write the…

Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y).

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

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: Consider the function f(x)=(x+1)(x–1)2, At what value of x will the graph of f cross the y-axis?…

A:

Q: Use Desmos to graph 1) y= Vx, 2) which is -f(x) 3) which is f(-x)

A: Hello! Thank you for the question. We will answer the first question since the exact one wasn't…

Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: h) f(x) = |Inx|

A: Sketch the following function showing in the given expression.  f(x) = 1/|lnx|

Q: For sketching the function y = 3-e² 2e² determine the following

A: Note: As you asked only for subparts 4, 5, 6, and 7 so, I answered here only that.

Q: Find the equation of the line tangent to the graph of f(x) = 3 - 2x at x = 3. Provide your answer…

A: The given curve is fx=3-2x and point is x=3 The slope of tangent on a curve f(x) at x=a is given by,…

Q: Write the equation of the line tangent to the graph of f (x) = -3x² + 5x + 1 at x = 1 and use it to…

A: We have to find the tangent line equation and also we have to approximate f(1.2).

Q: 2. Sketch the graph of the function (b) ƒ(x, y) = Vx² + y? – 1 -

A: our objective is to draw the graph.

Q: Shasta was working at differentiating a function p(x) and they found that p'(0) = In Unfortunately,…

A: We will determine the value of the constant a as following.

Q: Use the graph of f(x) = ex to obtain the graph of g(x) = eX. %3D %D

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.