Determine whether the given function is continuous. If it is not, identify where it is discontinuous. You can verify your conclusions by graphing the function with a graphing utility. 4x2 + 3x + 2 g(x) = x + 2

Q: Sketch the graph indicating maxima, minima, asy 4-x³ function: f(x) = x3

A: Given: f(x)=4-x3x3

Q: . The graph of the function f(x) = ax2 + bx + c has vertexat 10, 22 and passes through the point 11,…

A: We have  fx=ax2+bx+c To find the vertex of the quadratic equation, differentiate it and equate it to…

Q: Is the point (1/2 , - 3/5) on the graph of the function h(x) = (x2 - 1)>(x2 + 1)?

A: The given function is: hx=x2-1x2+1 To check the point (12 ,-35) is on the graph or not, put x=12,…

Q: Suppose the point (0, b) is on the graph of f(x) = -x +1, then the value of b is

A: We have to find value of b.

Q: True or false: The graph of the reciprocal function f(x) =1/x has a break and is composed of two…

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Q: Suppose you are given a formula for a function fpxq, and you are asked to find all the critical…

A: Suppose, Given - a formula for a function f(x) Critical Points: Critical point of a function are the…

Q: Use the graph of f(x) = x3 to obtain the graph of h(x) = (1/2)x3.

A:

Q: (b) Determine the discontinuities of the following functions and state why the function fails to be…

A: Given function is not defined at x=0

Q: If f(x) = x3 - 2x - 5, find f(2) and f(3). Then explain why the continuous graph of f must cross the…

A: Given  The function is f(x) = x3 - 2x - 5 .

Q: Find the intervals on which f (x) = x(x + 2)(x − 3) is positive by plotting a graph.

A: The graph of the given function is shown in the figure below.

Q: Determine the open intervals on which the graph is concave upward or concave downward.…

A: Given:    fx=20x2+3

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Asymptote is a line along which the function tends to infinity or minus infinity. Horizontal…

Q: Given the graph below, what can you say about the function at x = -2? -10 Not Continuous Continuous

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Q: y = x42x³

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Q: 1. Find x- and y- intercepts of the graph of f, if it has any.

A: Note: As you have posted the multiple numbers of questions, so we are going to solve the 1st…

Q: Sketch the graph of the function f. -{"2x+3 Sx - 6 if x s 3 if x > 3 (x)

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

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Q: Find all values of x, if any, where the function f(x) = x5 - 5x3 - 20x - 2 has local maximum and…

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Q: Find the absolute maximum and absolute minimum values of the function f(x) = -x3 + 12x + 6, over the…

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Q: Determine the intervals of concavity for the graph of f(x) =  lnx/x

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Q: Find the point on the graph of f(x) = √x that is closest to the point (6, 0).

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Q: By inspecting the graph of the function, find the absolute maximum and absolute minimum on the given…

A: From the given problem:   hx=x2-1x∈-4,5   Now differentiate the given function with respect to x and…

Q: Sketch the graph of the following function and find any discontinuities x2 – 1 f(x) = x - 1

A: fx=x2-1x-1 Since the value of numerator and denominator is zero when x=1, therefore the graph must…

Q: Find the absolute maximum and minimum values of the following function. If there are multiple points…

A: f(x)=6xx-x2 To find out absolute max  or min, take derivative with respect to x Apply product rule…

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: State whether the graph of fx) = + 7* + 10x has infinite discontinuity, jump discontinuity, point…

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Q: The graph f(x)- x² is transformed to create m(x) - f(bx)², where "b" is less than 1 but greater than…

A: Given function is                                                                         f(x)=x2…

Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = 2lxl.

A: Solution: Consider the graph of function f(x) = x which shows in the pink color below. Now, define…

Q: Find and label as minimum or maximum the stationary points for: f(x)-x -20х+105

A: We will solve the problem

Q: 11. Sketch the graph of the following function. f(x)= x³6x² - 9x [1]x- and y-intercepts

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

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Q: Determine where the graph of f(x) = |x - 3| is increasing and where it is decreasing.

A: To determine: The intervals where the function f(x)=x-3is increasing and decreasing. Given…

Q: Determine the open intervals on which the graph is concave upward or concave downward.…

A: Concave upward on (-inf,-6) and concave downward on (-6,inf).

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: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0, 2)

A: Given: f(x)=x2 ,        0,2

Q: f(x) : 1

A: The given function f(x)=1x2

Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: If f(x)=- +60, then what is the set of x values for which f has a relative maximum?

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Q: The graph of function f(x) = x – 9x² + 7x is concave upwards on (-0, c0) O (-∞, 3) O (3, 0) O None

A: Given function is  f(x)= x^3 - 9x^2 + 7x

Q: Find the intervals of concavity of the function g(x)=2x4+9x3

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Q: Find the open intervals on which the function is increasing or decreasing.       y = x√(16 − x2)

A: The given function is , y=x16-x2

Q: If f (x) is the function whose graph is shown, on which interval is fincreasing? Use cursor to…

A: f(x) is the function whose graph is shown, on which interval is f increasing?

Q: The graph of f(x)=x^2 rises or falls to the left? And does it rise or fall to the right?

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Q: Find x and y intercepts,intervals of monotoncity,local exterme value,intervals of…

A: Substitute x=0 and y=0 separately and solve for y and x respectively. Determine the critical points.…

Q: On which intervals is the function f(x)=-2x^(3) +3x^(2) +36x+4 increasing? Do not draw a graph.

A: The objective of the question is determine the interval in which the given function is increasing.

Q: Find the open intervals on which the function is increasing or decreasing.        h(x) = 12x − x3

A: Given function - h(x) = 12x-x3let's find the critical point of the function h(x) , by h'(x) =…

Q: The following is a graph of f'(x). At which value of a does f(x) have a maximum? y=f(x) -5 -2

A: The derivative of a function has a great importance in determining the analytical nature of the…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.