A water feature on a fountain follows a parabolic path and is represented by the function f(x) = -x(x – 8), which models the vertical distance as a function of the horizontal distance in feet. According to the graph of the function, the greatest height the water reaches is feet?

Q: Sketch the graph of the function. (4 - x2, x < -2 h(x) = 5+ x, -2 <x < 0 %3D 2+1, x 2 0 y

A: Given : for x &lt; -2 it is parabola opens downward as  sign of x2 is negative: for [-2, 0) it is…

Q: Sketch the graph of f.

A: The function fx=ex2

Q: Sketch the curve: f(x) = x* – 6x²

A: given function f(x)=x4-6x2we have to sketch the curve put the value of x=-2  , we get f(-2)=-8 put…

Q: A man drives from Detroit to Chicago, say 300 mi., at an average speed of 60 mi. per hr., stops 1…

A: Given : A man drives from Detroit to Chicago, say 300 mi., at an average speed of 60 mi. per hr.,…

Q: Sketch the graph of the function y = 3−∣x∣

A: We make a table for the given function

Q: If a baseball is projected upward from ground level with an initial velocity of 96 feet per second,…

A:

Q: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate…

A: Explanation: Given that,  Rate of snowstorm first two hours = 1 inches/hours Rate of snowstorm next…

Q: Find a function f whose graph is a parabola with the given vertex and that passes through the given…

A: Given the vertex (h, k) = (2,-1) The parabola

Q: Sketch the graph of the function. Jx+ 3, xs -5 g(x) 4, x > -5

A: Given,          The function is gx=x+3x≤-512x-4x&gt;-5

Q: Sketch the graph of the function. (Restrict your graph of the function to the domain [0,5).) gx) = 5…

A: We need to plot the graph of the given function.    gx=x   ,    x∈[0,5)

Q: Graph the functions f(x) = 2x and g(x) = 2x – 3 in the same rectangular coordinate system. Select…

A: The graphs of the function f(x) = 2x and g(x) = 2x - 3 are as follows:     The green line…

Q: Sketch the graph of the function and state its domain.

A: Given a function f(x)=ln 2x To find the domain : The domain is given by all the values of x where…

Q: List the x-values in the graph at which the function is not differentiable. -3

A: In this question with the help of graph theory we have to find the points where function is not…

Q: Sketch the graph of the curve f(x)=3x³ - 3x + 2

A:

Q: Asymptotes: x = 3 and y = -2.

A: Given: Asymptotes are x = 3 and y = -2

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

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Q: 4. Using at 7 points, graph the function f(x)=2x

A:

Q: Estimate the slope of the function (x) at x = -1 using the graph below.

A: Given function is passing through (-1,-1) and (0,-1) and function f(x) has two points at which…

Q: Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist?

A:

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

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Q: What is the zeros of this function?

A:

Q: Define the graph of the function f(x) = x^2?

A: fx=x2 x f(x) 0 0 1 1 2 4 -1 1 -2 4

Q: Use the function’s equation, f(x) = -x2 + 14x - 106 and not its graph, to find; a. the minimum or…

A: we have been given  f(x) = -x2 + 14x - 106 we have to tell the minimum and maximum value . also we…

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: The graph of y= {x) is compressed horizontally by a factor of reflected in the y-axis. What is the…

A: We have to find the equation of new function in terms of f(x).

Q: How do you prove step by step that this equation: y=2x+1 is a function?

A: The solution are next step

Q: Does the function g(x)=2-x  approach a certain real number as the value of x increasing positively?…

A: Given - g(x) = 2-x To find - Does the function g(x) approach a certain real number as the value of x…

Q: Find the x- and y-intercepts of f and sketch the graph. Approximation of graph will suffice. 1) f(x)…

A: For x-intercept : put y = 0 and For y-intercept : put x= 0

Q: Sketch the graph of f.

A: Given: fx=2x+12 For drawing graph of given function, we use graphing utility  So, graph of given…

Q: The graph of f(x)=3xf(x)=3x  is reflected about the yy-axis and stretched vertically by a factor of…

A: Given,         The graph of f(x)=3x  is reflected about the y-axis and stretched vertically by a…

Q: Sketch the graph of f(x) = 1/(x2+1)

A: The graph of f(x) = 1/(x2+1)

Q: Find a function f whose graph is a parabola with the given vertex and that passes through the given…

A: The standard equation of the parabola having vertex at (h, k) is given by, y-k=a(x-h)2

Q: If a projectile is fired straight upward from the ground with an initial speed of 128 feet per…

A:

Q: Is the point (4, 14) on the graph of the function g(x) = (x2 + 4)&gt;(x + 2)?

A: Given inequality is: gx=x2+4&gt;x+2 Given point is (4, 14).

Q: Sketch the graph of the function f(x) = (2x − 1)/(x + 1)(x − 3)

A:

Q: g(x) = In(4x - 3)

A:

Q: function

A: We will solve the problem.

Q: Determine the “x-intercept” of the Function (Assume that a graph continues at both ends if it…

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Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A:

Q: Sketch the curve. Show your solutions. f(x) = x4 - 6x2

A: Consider the given: fx=x4−6x2Apply exponent rule:     ab+c=abacfx=x2x2−6x2Factor out common term…

Q: Sketch the graph of the function: (plot at least 4 points on the graph) -5x +2 ,x<0 F(x) = 1-x²-2 x…

A:

Q: Sketch the graph of f(x)= square root(-1-x) by hand, without calculator

A: Choose some value of x and find the corresponding values of f(x) as shown below table.

Q: ) Sketch the curve: f(x) = x* – 6x²

A: Given function is fx=x4-6x2

Q: Find the equation of the horizontal asymptote for the function f(x)= 2 - (x / x2 -25)

A:

Q: . Find the length of the graph of the function f (x) =x* + x2 -<x < 3. on the ir

A: The length of the graph of y=f(x) from x=a to x=b is given by:∫ab1+f'(x)2dx f'(x):…

Q: The path of a diver is modeled by f(x) = - :-x² +24x+9 where f(x) is the height (in feet) and x is…

A:

Q: Sketch the graph of the function. y = e−x2

A: we have to sketch the graph of y=e-x2

Q: Express the solution as a piecewise-defined function and think about what happens to the graph of…

A: (c) In this question, we have to use the property of the Heaviside unit step function about t=5.…