Select a few x x values, and plug them into the equation to find the corresponding y y values The x x values should be selected around the vertex Tap for more steps Replace the variable x x with − 1 1 in the expression f ( − 1) = ( − 1) 2 − 2 f ( 1) = ( 1) 2 2 Simplify the resultMath Input NEW Use textbook math notation to enter your math Try itThe graph of a function f is given Sketch the graphs of the following transformations of f (b) y = f(x) − 3 (c) y = 2f(x) (d) y = −f(x) 5 (e) y = f(−x) (f) y =1/2f(x − 4) Question The graph of a function f is given Sketch the graphs of the following transformations of f
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F(x)=x^2-2x-3 graph-Graph f(x)=x^32x^2x2 Find the point at Tap for more steps Replace the variable with in the expression Simplify the result Tap for more steps Simplify each term Tap for more steps Raise to the power of Raise to the power of Multiply by Multiply by Simplify by adding and subtracting Tap for more stepsUse a graph of f(x) to determine the value of f(n), where n is a specific xvalueTable of Contents0000 Finding the value of f(2) from a graph of f(x)002
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Calculate the vertex and the x and yintercepts and then sketch the graph f(x)= x^23 Step 1 Your equation is almost in vertex form f(x) = a(xh)^2 k Rewrite it slightly to get f(x)= 1(x0)^23 We see that a=1, h=0, and k=3 Step 2 Find the vertex The vertex is at (h,k) or (0,3) Step 3 Find the yintercept Set x=0 and solve for y f(0)= 0^23 =03=3 The yintercept is at (0,3Graph f(x)=(x2)(x3)(x1) Find the point at Tap for more steps Replace the variable with in the expression Simplify the result Tap for more steps Simplify each term Tap for more steps Raise to the power of Multiply by Multiply by by adding the exponents Tap for more steps The graph of #f(x)=x^2# is called a "Parabola" It looks like this One of the ways to graph this is to use plug in a few xvalues and get an idea of the shape Since the x values keep getting squared, there is an exponential increase on either side of the yaxis
We are given the quadratic function y = f (x) = (x 2)2 For the family of quadratic functions, the parent function is of the form y = f (x) = x2 When graphing quadratic functions, there is a useful form called the vertex form y = f (x) = a(x −h)2 k, where (h,k) is the vertex Data table is given below (both for the parent function andGraph the functions f(x) = x 22x 2, g(x) = f(x), and h(x) = f(x) Answer Exercise 5 Look again at the graph of f(x) = x 22x 2 from Exercise 4 This graph is the result of shifting the graph of x 2 Find the shifts and show that the formula obtained from shifts is equal to the formula for f Answer Exercise 6 Find a function whose graph isAll equations of the form ax^{2}bxc=0 can be solved using the quadratic formula \frac{b±\sqrt{b^{2}4ac}}{2a} The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction
F ( x) = 3 x 3 − x 2 By Rational Root Theorem, all rational roots of a polynomial are in the form \frac {p} {q}, where p divides the constant term 2 and q divides the leading coefficient 3 One such root is 1 Factor the polynomial by dividing it by x1 Polynomial 3x^ {2}3x2 is not factored since it does not have any rational rootsGraph f (x)=2 (3)^x f (x) = −2(3)x f ( x) = 2 ( 3) x Exponential functions have a horizontal asymptote The equation of the horizontal asymptote is ySOLUTION graph the function?
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Graph a quadratic function using transformationsGraph f (x)=2x3 f (x) = 2x − 3 f ( x) = 2 x 3 Rewrite the function as an equation y = 2x− 3 y = 2 x 3 Use the slopeintercept form to find the slope and yintercept Tap for more steps The slopeintercept form is y = m x b y = m x b, where m m is the slope and b b is the yintercept y = m x b y = m x bSolution for 2 2 lim f(x) 2 For the graph above, find Select one a 1 b 4 C O d 3 e 2 2
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How to graph a quadratic function using transformationsYou have to simplify the given equation to make the graph, as we know that the graph of modulus/absolute function consists of straight lines, we will deduce equations of straight lines from the given function f(x)=4 x2 3 we'll first findSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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125x3 − 150x2 60x − 8 View solution steps Solution Steps f ( x ) = ( 5 x 2 ) ^ { 3 } f ( x) = ( 5 x − 2) 3 Use binomial theorem \left (ab\right)^ {3}=a^ {3}3a^ {2}b3ab^ {2}b^ {3} to expand \left (5x2\right)^ {3} Use binomial theorem ( a − b) 3 = a 3 − 3 a 2 b 3 a b 2 − b 3 to expand ( 5 x − 2) 3 125x^ {3}150x^ {2F (x – b) is f (x) shifted b units toGraph a function with absolute value with a horizontal shift
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Axis of Symmetry x = 3 x = 3 Directrix y = −1 4 y = 1 4 Select a few x x values, and plug them into the equation to find the corresponding y y values The x x values should be selected around the vertex Tap for more steps Replace the variable x x with 2 2 in the expression f ( 2) = ( 2) 2 − 6 ⋅ 2 9 f ( 2) = ( 2) 2 6 ⋅ 2 9Purplemath The last two easy transformations involve flipping functions upside down (flipping them around the xaxis), and mirroring them in the yaxis The first, flipping upside down, is found by taking the negative of the original function; " " Please read the explanation " " Given the exponential function color(red)(f(x)=3^(x2) Before graphing this function, create a data table The table should contain values for color(red)(x, corresponding values for color(red)(y=3^x) and color(red)(y=3^(x2) We include the base function color(red)(y=3^x, since it provides an opportunity to examine the behavior of both the graphs
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Note, first, that the function will never be valued below 1 This is because (x2)^2>=0 Now, when x=2 we have f (2)=1 x=2 is the absolute minimum value of x because any other number will result in a square greater than 0 So we have (2,1) as the vertex Question 3 3 f(x) 9(2) 2 3 3 3 3 3 3 Use the graphs to estimate the derivative of k(x) = f(x) at x = 0 8(x) Ok' (0) = 15 Ok'(0) = 52 O k'(0) = 64 Ok' (0) = 68 O k'(0) = 15 (a) Find the slope of the graph of f(x) = 1 – et at the point where it crosses the xaxis The slope is (b) Find the equation of the tangent line to the curveTranscribed image text The function f is continuous everywhere and F"(x) = (x – 1) (x – 2)2(x – 3)3 (a) Find all intervals where the graph of f is concave down (b) Find the xcoordinates of inflection points on the graph of f
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Steps Using Derivative Rule for Sum f ( x ) = 3 x ^ { 2 } 1 f ( x) = 3 x 2 1 The derivative of a polynomial is the sum of the derivatives of its terms The derivative of a constant term is 0 The derivative of ax^ {n} is nax^ {n1} The derivative of a polynomial is the sum ofIn this math video lesson I review how to graph the exponential equation y=2^x by making a table The table helps when graphing these types of equations #eThat is, the rule for this transformation is –f (x) To see how this works, take a look at the graph of h(x) = x 2 2x – 3
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To zoom, use the zoom slider To the left zooms in, to the right zooms out When you let go of the slider it goes back to the middle so you can zoom more You can clickanddrag to move the graph around If you just clickandrelease (without moving), then the spot you clicked on will be the new center To reset the zoom to the original clickThe equation is in standard form xf=x^ {3}4x^ {2}11x30 x f = x 3 − 4 x 2 − 1 1 x 3 0 Divide both sides by x Divide both sides by x \frac {xf} {x}=\frac {\left (x5\right)\left (x2\right)\left (x3\right)} {x} x x f = x ( x − 5) ( x − 2) ( x 3) Dividing by x undoes the multiplication by x Table 251 Example 251 Sketch the graph of g(x) = √x 4 Solution Begin with the basic function defined by f(x) = √x and shift the graph up 4 units Answer Figure 253 A horizontal translation 60 is a rigid transformation that shifts a graph left or right relative to the original graph
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Here is a picture of the graph of g(x) = 3(x)1/2 Since c = 3 > 1, the graph is obtained from that of f(x) = x1/2 by stretching it in the ydirection by a factor of c = 3 Reflection about the x axis The graph of y = f (x) is the graph of y = f (x) reflected about the x axis Here is a picture of the graph of g(x) = (x 2 1)In this graph, f (x) has been moved over three units to the left f (x 3) = (x 3) 2 is f (x) shifted three units to the left This is always true To shift a function left, add inside the function's argument f (x b) gives f (x) shifted b units to the left Shifting to the right works the same way;Graph f(x)=(x2)^23 Find the properties of the given parabola Tap for more steps Use the vertex form, , to determine the values of , , and Since the value of is positive, the parabola opens up Opens Up Find the vertex Find , the distance from the vertex to the focus Tap for more steps
F X F X 2 F X 2
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Graph of f (x)=2/3x2 Below you can find the full step by step solution for you problem We hope it will be very helpful for you and it will help you to understand the solving process If it's not what You are looking for, type in into the box below your own function and let us find the graph of it The graph of f (x)=2/3x2 represents a graphShort Solution Steps f ( x ) = 3 x ^ { 2 } \frac { 3 } { x ^ { 2 } } f ( x) = 3 x 2 − x 2 3 To add or subtract expressions, expand them to make their denominators the same Multiply 3x^ {2} times \frac {x^ {2}} {x^ {2}} To add or subtract expressions, expand them to make their denominators the same Multiply 3 x 2 times x 2 x 2 The correct answer is C 1 Explanation Using the graph for f (22), we go to 22 on the xaxis This will lie between 2 and 3 We then go up to see where it we "meet" the graph This happens at y=1, so that is our answer apsiganocj and
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F (X)= (x2)^21 You can put this solution on YOUR website! Both are functions, only difference (equationwise) is the cvalue, which causes g(x) to translate 2 units down The only difference between the two (equationwise) is the cvalue The cvalue controls the vertical translation of a function With 2 as the value, g(x) goes down 2 units We can prove this with a graph graph{(yx^2)(yx^22)=0 1616, 1231, 746, 677} The graphF(2)=3 means that when you substitute x=2 in the equation y = f(x) like this y = f(2) That the value of y is 3 because f(2) = 3 That means that the graph contains the point (x,y) = (2,3) So we plot that point (2,3) and the line x=3, which is a vertical line through 3 on the x axis, the green line below We want to reflect that point across the green line
1
Solution Graph The Quadratic Function F X X 3 2 1
Draw the graph of the following function {eq}f(x)=x^23 {/eq} Transformations of Graphs We know the graphs of a few basic functions, such as the square root functionPrecalculus Graph f (x)= (x3)^32 f (x) = −(x − 3)3 2 f ( x) = ( x 3) 3 2 Find the point at x = 1 x = 1 Tap for more steps Replace the variable x x with 1 1 in the expression f ( 1) = − ( ( 1) − 3) 3 2 f ( 1) = ( ( 1) 3) 3 2 Simplify the result Tap for more steps0 = x 3 – 8 = (x – 2)(x 2 2x 4) 0 = x – 2 2 = x I Much of the above graph (especially the middle part) would not show up on the graphing calculator, so a lazy student would be "caught" when he didn't include that middle part in his graph For this reason
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Correct answer to the question On a piece of paper graph f(x) = {1 if 1Graph f(x) together with its tangent and normal lines at x= 4 ( 4 8 3 Plot the curve x 13 = 6 xy together with the tangent to the curve at the point 3' 3 4 Calculate the derivative of the function f(x) = sin(x) and plot the function and its derivative on the same graph Describe the relationship between the two graphs 1 lax 5Let us start with a function, in this case it is f(x) = x 2, but it could be anything f(x) = x 2 Here are some simple things we can do to move or scale it on the graph We can move it up or down by adding a constant to the yvalue g(x) = x 2 C Note to move the line down, we use a negative value for C C > 0 moves it up;
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C < 0 moves it downSketch the graph of f(x)=x^22x3 finding the vertex, axis of symmetry and all intercepts*Note The student uses a formula to find the ycoordinate of the
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