Given f(x) = -x4 + 16x2, solve the following:  a. Use the Leading Coefficient Test to determine the graph’s end behavior. b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. c. Find the y-intercept. d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.

Q: Find the x-intercepts of the given function.  y = 3x2 + 10x + 3

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Q: Albert was tasked to graph f (x) = x3 – 6x² + 9x + 1, and his graph is shown. Would you agree with…

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Q: For what values of k will the graph of y=9x2 +3kx+k have no x-intercepts?

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Q: Find the value of x for which y = x5 – 5x3 – 20x – 2 will have a maximum point.

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Q: • Determine and draw the graph of the following equation in R3 : x2 + 212 + 2 8x + 12y – 2z + 35 = 0…

A: This is a problem of multi variable calculus, 3D geometry.

Q: The graph of f(x) = −12x2 − 1 has no x-intercepts.Determine whether the statement is true or false.…

A: x-intercept: The point at which the graph intersects the x-axis is called the x-intercept. The…

Q: The graph of y=5x*-x³ has a point of inflection at (A) (0, 0) and (4, 256) B (0, 0) and (3, 162) (3,…

A: Given graph,y=5x4-x5Aim : To find point of inflection.

Q: Sketch the graph of 3x - 2y = 12 using the slope-intercept method:

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Q: Graph f(x) = x2 + 4x - 5 by determining whether thegraph opens up or down and by finding the vertex,…

A: Given, f(x)=x2+4x-5 function intercept on x-axis at y=0 x2+4x-5=0x2+5x-x-5=0xx+5-1x+5=0x+5x-1=0 so…

Q: Find the point on the graph of y2 - xz2 = 4 nearest the origin.

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Q: . Graph f(x) = 2x2 - 4x + 1 by determining whether itsgraph opens up or down and by finding its…

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Q: The revenue of a charter bus company depends on the number of unsold seats. If the revenue R(x) is…

A: Given: The revenue of a charter bus company is,  Rx=8000+70x-x2. Here, x is the number of unsold…

Q: Match the equation with its graph. x² + 2z2 = 1

A: Graph of  x^2 +2z^2 =1 is

Q: Based on the difference in y-values, identify the graph as linear, quadratic, exponential, or…

A: Plotting the values on x-y plane we see that the following result.   The curve will proceed and cut…

Q: Find the x-intercepts of the given function.  y = 2x2 + 5x + 2

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Q: Find the x- and y-intercepts of the graph of y = x3 − 4x.

A: Concept - We obtain x-intercept by putting y=0, and the points obtained are x, 0.We obtain…

Q: Use the five-step strategy to graph f(x) = 2(x + 2)2(x - 3).

A: The given function is a polynomial function, so it is continuous everywhere and thus, it has no any…

Q: Graph f(x) = – 2x² – 20x – 42 below by first selecting - - the correct shape, clicking the vertex,…

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Q: I need to graph f(x)= x^2+3. And I need to know why it's graphed that way.

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Q: Suppose that the x-intercepts of the graph of y=f(x) are 2 and 6. What are the x-intercepts of…

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Q: (b) Find the number of points of intersection of the graph of y = = -x + 6x -(a + 9) and the x-axis.

A: It is given that the equation of the parabola is y=-x2+6x+a-9. We have to find the number of points…

Q: 9- -x2 www Ay 2. 4 x 田 田

A: Given :— x — 6 = —x2 In Graph, x = 2 , 4 , —2 , —4

Q: Find the intercepts of the graph of h(x) = 3 | x + 2 | - 1.

A: The x-intercept of a graph is a point where the graph meets the x-axis. The y-intercept is the point…

Q: For what values of x does the graph of y=3x5+10x4 have a point of inflection?

A: f(x)= 3x5 + 10x4 differentiate with x f'(x)= 15x4 + 40x3 f''(x)= 60x3 + 120x2 = 60x2(x+2)

Q: Use the five-step strategy to graph f(x) = x3 - 3x2.

A: The given function is x3-3x2 The main objective is to plot a graph for the given function x3-3x2…

Q: Graph f(x) = x² – 8r + 15 below by first selecting the correct shape, clicking the vertex, then…

A: Let y=f(x), ⇒y=x2-8x+15⇒y=x2-8x+16-1⇒y+1=(x2-8x+16)⇒(y-(-1))=(x-4)2 Which is comparable to…

Q: Suppose that the x-intercepts of the graph of y = f1x2 are- 5 and 3.(a) What are the x-intercepts of…

A: Consider the provided information, y=fx. And the x intercept is -5 and 3. So, Given the x-intercepts…

Q: Find the x-intercepts of the given function.  y = 4x - 4x2 - 1

A: given the function: y=4x-4x2-1For finding the x- intercept , y=0

Q: For Exercise, estimate the x- and y-intercepts from the graph. -3 – –1

A: Where the graph cuts/touch the x-axis those are the x-intercepts From the graph, we see…

Q: What is the piece-wise equation and domain for the 1t section of the graph? f(x)

A: NOTE: Refresh your page if you can't see any equations. . for the first part, the x-intercept is…

Q: Which equation has a graph that is parallel to and has a y-intercept exactly 2 units away from the…

A: We have to find the equation of line

Q: Use the crossing- graphs method to solve the equation below. 3^x + x = 2^x +3

A: We graph y= 3x+x and y=2x+3 using a graphing calculator.

Q: Is the graph of r(x)=4x3−2x2+9x−2 concave up or down at the point with x-coordinate −1?

A: Given          r(x) = 4 x³ - 2x² + 9x - 2 For checking concave up or down we have to differentiate…

Q: Graph f(x) = x² – 8x + 12 below by first selecting the correct shape, clicking the vertex, then…

A: f(x)=x2-8x+12y=x2-2x(4)+42+12-42y+4=(x-4)2 hence the vertex is (4,-4)for x intercept…

Q: Find the slope and y-intercept of the graph ofy = -6x + 3.

A: We have to find slope and y-intercept of the graph of y=-6x+3. We know equation of line in form of…

Q: To find the x-intercepts, let y be zero and solve for x. (0) x- 49x %3D 0 = x(x2 - 49) = x(x2 - 72)…

A: From the second step we see that

Q: How many times does the graph of y = ax + b with a + 0 intersect the x-axis?

A: Given that, y=ax+b

Q: Plot the graph of Y=3x – 4 between x= -2 and x=4

A: Given equation: Plot the graph of y = 3x-4: The graph is:

Q: Match the equation with its graph. -x2 + y2 - z? = 1 ZA

A: -x2+y2-z2=1

Q: Find the extreme of the values of the function  y = x2 - 2x + 1

A: Given:y=x2-2x+1

Q: How do you obtain the graph of y = f13x) from the graph of y = f(x)?

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Q: Explain the effect that the constant a has on the graph of y = ax². Be sure to consider a 0.

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where (h,k) is the vertex of the parabola…

Q: Given f(x) = -5x² – 7x + 2, without graphing, determine whether it has a maximum value or minimum…

A: Given equation  f(x) = -5x2-7x+2 Whether the equation has maximum or minimum value is evaluated as…

Q: 9. If you were to graph f (x) = 2x2 + 4x – 6 , what would the coordinates of the vertex be? What…

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Q: Based on the difference in y-values, identify the graph as linear, quadratic, exponential, or…

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Q: What is the x-coordinate of the point of inflection on the graph of y = x'- 2x² + 7?

A: Given,           y=23x3-2x2+7

Q: Determine whether the graph of q(x)=−6x3−7x2+8x+2 is concave up or down at the point with an…

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Q: Make a table of values, and sketch a graph of the equation. 4y = -x2

A: Given: 4y=-x2

Q: How does the value of a affect the graph of y = ax? if a s 0?

A: The given equation is,     y=ax2

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.