61. If f(x) = 2x² + 5 and g(x) = 3x + a, find a so that the graph of fo g crosses the y-axis at 23.

Q: Suppose (P. O) is the point on the graph of y =Vx closest to (1. 0) - What is the value of P+ 1-

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Q: Sketch the graph of y = f(x + 2) - 1, where f(x) = x 2 for -2 ≤ X ≤ 2.

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Q: Find the length L of the graph of 3 ( a) f(x)=x/2 +1 for 0<x< 4

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: The area of the largest rectangle that can be drawn with one side along the x-axis and two vertices…

A: The diagram below shows the rectangle as mentioned in the problem, The rectangle is symmetric about…

Q: 2) y=-5+ Vx+ 1

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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: For what value of x does the function f(x)=1/3x3-4 attain the absoulte maximum in tyhe interval…

A: Put derivative zero for maxima and minima

Q: 3. Discuss how to transform the graph of y = x2 in order to obtain the graphs of #2a and #2b above.…

A: 3(a):

Q: Sketch the graph of y = f (x + 2) − 1, where f (x) = x2 for −2 ≤ x ≤ 2.

A: To sketch the graph

Q: Find the equation of the secant line on the curve f(x) = -x²+2 passing through the points xo = -1…

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Q: The graph of y = 5f(x) is obtained by a/an _______stretch of the graph of y = f(x) by multiplying…

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Q: Find an equation for the graph sketched below 7- 4- -5 -4 -3 -2 -,VI 2 3 4 5 -2 -7- -8+ f(z) =| %3D…

A: Consider the provided graph, We need to find the equation of the above graph.

Q: - Find all k so that the graph of y = Er2 kx - + 9 is tangent to the x-axis. 4

A: We have to find all values of k such that the graph of this function will have tangent as x axis.…

Q: Find the point on the graph of the function x = √10y that is closest to the point (0, 4)

A: The given function and point are x=10y and (0, 4) respectively. The graph of the function x=10y is:…

Q: х3 — х2 — 12х x - - Sketch the graph of y = f(x) | ,2 x* - х — 2

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Q: The point of the given function at (2, -7) is found to be y = x3 – 2x2 – 4x + 1

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Q: A D Function "p" is in the form y = ax2 + c. If the values of "a" and "c" are both less than 0,…

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Q: V: Sketch the graph at: a) Jex)= X3 6) fex X x2-1 3/ x4.

A: a) fx=x3x-22b) fx=xx2-1c) fx=x2-123-x43

Q: {2*+1 if x<0 etch the graph of f(x)=X+3 EO

A: We will graph the problem.

Q: For what values of x is the graph of y=xe^(−2x) concave down?

A: Find first derivative using product rule and chain rule.

Q: Find the point on the graph of the function y = 4 - x2 that is closest to the point (0,2)

A: Find a point (x, y), closest to the function.

Q: 2. How does the graph of f (x) =- Vx+4 – 3 differ from the graph of y = - VX?

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Q: 7. Use the graph of f(x) → 3x² to obtain the graph of h(x) =x² .2

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Q: 1. How does the graph of f (x) = vVx – 2 differ from the graph of y = Vx+ 3 ?]

A: The value of sqrt(x-2) is differ from the value of sqrt(x+3).

Q: (d) Find the interval where the graph of y = x³ + 2x² – 4 is decreasing and concave - up.

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Q: 5. If f(x) = ax* + bx' +cx² + dx +e, determine a, b, c, d and e so that the graph of f will have a…

A: 5) Given:   f(x)=ax4+bx3+cx2+dx+e As f(x) passes through origin (0,0) then substituting (0,0) in…

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

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Q: For what value of x will the curve y = x3 - 3x2 + 4 be concave upward?

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Q: If f(x) = 3x^2 − 7 and g(x) = 2x + a, find a so that the graph off ◦ g crosses the y-axis at 68.

A: Given

Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

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Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

A: Use distance between point concept and then differentiate

Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

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Q: The degree of f(x) is [odd and the leading coefficient is negativev. There are real zeros and…

A: Consider the graph

Q: Suppose that / (3r-x²) dr=Ax³+ Bx+C, for constants A, B, C. What is the value of C if the curve…

A: The given integral ∫3x4-x2dx=Ax5+Bx3+C

Q: Suppose that the graph of x = f(y) lies to the left of the y-axis. Is f(y) dy positive or negative?

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Q: 2) Use DESMOS to graph Y = 10* + 3, show critical points. %3D

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Q: 1. Sketch the graphs of the following functions: N(a) y=x² y= 3x2 y = 4x y =-3x ² y=-4x2 y=ー ー=へ)…

A: Since you have posted question with multiple subparts , we will solve the first three subparts for…

Q: Explain how to identify the graph of : Ax2 + Cy2 + Dx + Ey + F = 0.

A: If an equation has a square form of the variable  or a square form of the variable  or a square form…

Q: 30. The graph of y = x³ + 21x² – x + 1 is concave down for (a) x 7 (e) x 7.

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Q: Use the given graph of y = f(x) to solve graph g(x) = f(x - 1) + 1.

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

A: our objective is to draw the graph.

Q: Sketch the graph of y = (x – 3)*(x + 1)³(x - 1) by finding its intercepts and its limits as x → o…

A: topic - functions

Q: Show that the graph of f(x)=(3-4x)/e^2x has minimum value at x=5/4.

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

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Q: The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x)…

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Q: Sketch the graphs of r(x) = and a(x) = |x|- 3 on the set of axes below. Determine, to the nearest…

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Q: If f(x) = 2sin (3x), the formula to compress the graph vertically by factor 4 followed by a…

A: Definition used -    If  graph of a function f(x) compressed vertically by factor a , then new…

Q: Is the graph of g(x)=4x^3+9x^2+7x+3 concave up or down at the point with x-coordinate −2?

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