Fill in the blank with the appropriate direction (left, right, up, or down). (a) The graph of y = f(x) – 9 is obtained from the graph of y = f(x) by shifting --Select--- + 9 units. (b) The graph of y = f(x – 9) is obtained from the graph of y = f(x) by shifting --Select-- A 9 units.

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: Match the function with its graph. f(z) = – 2(x – 3)² 6+ 4 -3 -2 -1 -6 -5 -4-3 -2 -1 -6 -3 -2 3 4 5…

A: The function is given by f(x) = -2x-32

Q: Which shows where the function is decreasing?

A: The graph of the function f(x) is shown. The function f is increasing if the derivative of function…

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: Which transformation from the graph of a function f(x) describes the graph of t)?

A:

Q: 11. Differentiate the function (use chain rule): y = x²(x-1)³(2x-5)² ;

A:

Q: Determine the function f represented by the graph of the line y=f(x) in the figuro. 10- 5- -10 10…

A:

Q: What are the x- and y-intercepts of a function, and how are they found?

A: The x-intercept is the length from origin to where the graph of the function cut the x-axis.   The…

Q: How might you restrict the domain of f(x) = x2, graphed in Figure 1.71, so that the remaining…

A: Given that, f(x)=x2 We have to Find How to restrict the domain of f(x)=x2  So that the remaining…

Q: SKetch graph : f(x) (2-x if xI

A: For  x&lt;-1f(x)=2-xat x=-2   y=f(x)=4at x=-3   y=f(x)=5 Plot this line on graph

Q: for the quartic function represented by this graph?

A: In the given question, the concept of quartic function is applied. Quartic Function A quartic…

Q: Match the function with its graph. y = 5(x + 2) - 4 5- -4 -6 -5 4 -3 -2 1 4 6 -6 -5 -4 - -2 -6 -5 4…

A:

Q: 104v 2 -10 -8 -6 -4 -2 0 4 6 8 10 -2 -4 -6 -8 -10 Match the graph with its function by translating…

A: topic - translation of a function

Q: If r is a zero of even multiplicity, how come the graph of f doesn’t just cross the x-axis at r?

A:

Q: Check the function y=x²+1 whether have a symmetry about x or y axis

A:

Q: Match the function with its graph. I II y 1 III IV (a) f(x) = x2 ---Select--- (Б) f(x) = x3…

A: use the basic concept of function and  graph we get the match.

Q: 3x-x - Show that the function y= 1+x? odd or even.

A:

Q: Sketch a graph of f(x) = – 1|x| %3D -

A:

Q: sketch the graph of function Xy-y-1=0

A: xy-y-1=0 we can draw the graph of the function

Q: Which is always a characteristic of the graph of a linear function?

A: Explanation of the solution as follows:

Q: Which of the functions has the y-axis as the line of symmetry?

A: Generally we check three kinds of symmetries for the graphs. Symmetry about X axis Symmetry about Y…

Q: Graph the function f(x) -sec 4+ 3 on the interval -27, 67|.

A: Consider the given function f(x) and all the values required to plot the f(x).

Q: Which transformation is used to obtain the graph of f(x)= -2X from grape of f(x) = 22?

A:

Q: 5- For the function f(x)=x³/3(x²-3) – 3/2, determine: a- The domain. b- The x and y intercepts. c-…

A: Given problem:-

Q: Sketch the graph of the function. (3x + 3, X ≤ -1 k(x) = 3x²-2, -1 1 y

A:

Q: Find the point at which the line f() = --1 intersects the line g(a) 2 + 8

A: Two lines f(x)=-x-1 and g(x)=2x+8 , we have to find the point at which both lines intersects.

Q: Sketch a graph of: f(x) = 2|x+3|– 1 5+ %3D 4 -5 -4 -3 -2 -1 4 5 -1 -2- -3 -4 -5+ 2. 3. 2.

A: Answer is mentioned below

Q: Exercises 38–40 will help you prepare for the material covered in the first section of the next…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the range of the function y = -2|x – 3| + 2. O (-∞,2] O (-∞, ∞) O (-∞, 2) O [2, 0) O [3, ∞) O…

A:

Q: Match the function with its graph. I II y y 1+ III IV ++ i (a) f(x) = x2 ---Select--- (b) f(x) = x3…

A:

Q: Match the function with its graph. y = 3(x + 3) – 2 6- -5- 5 4- -6 -5 5 6 -6 -5 -4 -6 -5 5 6 to -2…

A: Given that the equation. So first simplyfy it. Then here a&gt;0 so it is upward parabola and…

Q: Sketch the graph of the floor function f(x)= |x +1|| over the interval [-3, 3)

A:

Q: Sketch the graph of the functi y= (]x-1|)/(x-1)?

A:

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

A: As we see in the given question, there is only graph so according to this graph for you intercept We…

Q: Sketch a graph of the function f(æ) = 3 sin(,2) – 1 6+ 4 -9 -8 -7 -6 -5 -4 -3 -2 -1 2 3 4 5 6 -2 -3…

A:

Q: y = (x +2)x² - 1

A:

Q: Find the equation of the slant asymptote for the function f(x)=x^2-x/x-2 y=

A:

Q: Sketch a graph of: f(x) = 2|x – 1|- 4 5+ 2 -4 -3 -2 -1 -1 I 2 -5 3 4 -2 -3- -4 -5+ Clear All Draw:…

A:

Q: Graph of f 8. 7. 6. 5. 3. -10 -9 -8 7 -6 -5 -4 -3 -2 -1 3 4 5 8. 10 -1 -2 -3 -4 -5 -6 -8- 6.

A: The graph of a function f is given as, The objective is to find the value of ∫-49fxdx.

Q: Sketch the graphs of f and g in the same coordinate plane. x) -5*, g(x) logs x y y

A:

Q: determine all horizontal and vertical asymp-

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: The slope y-intercept form of a linear relation is represented by y=mx+by=mx+b.  Which equation…

A: Solution: The objective is to find equation shows x isolated correctly for this formula

Q: Supposed that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions…

A: Given Data: The number of females in the US under 18 is: N=0.140x+36.4 The slope of the graph of the…

Q: The graph of f is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same…

A:

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

A: Given function is fx=x4-6x2

Q: The graph of f- is a reflection of the graph of f about the line whose equation is y = x. y 0. x 0.…

A: We want the inverse of function by reflection

Q: Sketch the graph of f(0)= – 3tan(20)+1. %3D

A: To sketch the graph

Q: Find the gradient of the graph a) y = 6-3x where x = 5 )y= 12 + x-3x? where x = - 3

A: Find the gradient of the function

Q: The graph of linear function f passes through the point (1,-9) and has a slope of -3.   What is…

A: Given for a linear function , Slope =-3 and passes through (1,-9)

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:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.