Microvillus Inclusion Disease Pathology, Things To Do In Martinsburg, Wv This Weekend, How To Cook Oat Groats Uk, Jin Ramen Mild Vs Spicy, Perfect Simple Plan Acoustic, Affordable Dentures Coupons, What Happened To The Captain Of The Costa Concordia, " /> Microvillus Inclusion Disease Pathology, Things To Do In Martinsburg, Wv This Weekend, How To Cook Oat Groats Uk, Jin Ramen Mild Vs Spicy, Perfect Simple Plan Acoustic, Affordable Dentures Coupons, What Happened To The Captain Of The Costa Concordia, " />

vertical stretch equation

• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k. Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. give the new equation $\,y=f(\frac{x}{k})\,$. Vertical Stretch or Compression In the equation [latex]f\left(x\right)=mx[/latex], the m is acting as the vertical stretch or compression of the identity function. Transformations: vertical stretch by a factor of 3 Equation: =3( )2 Vertex: (0, 0) Domain: (−∞,∞) Range: [0,∞) AOS: x = 0 For each equation, identify the parent function, describe the transformations, graph the function, and describe the domain and range using interval notation. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function.In other words, we add the same constant to the output value of the function regardless of the input. When is negative, there is also a vertical reflection of the graph. $\,y=kf(x)\,$. ★★★ Correct answer to the question: Write an equation for the following transformation of y=x; a vertical stretch by a factor of 4 - edu-answer.com vertical stretch; $\,y\,$-values are doubled; points get farther away from $\,x\,$-axis $y = f(x)$ $y = \frac{f(x)}{2}\,$ vertical shrink; $\,y\,$-values are halved; points get closer to $\,x\,$-axis $y = f(x)$ $y = f(2x)\,$ horizontal shrink; and multiplying the $\,y$-values by $\,\frac13\,$. This causes the $\,x$-values on the graph to be DIVIDED by $\,k\,$, which moves the points closer to the $\,y$-axis. (MAX is 93; there are 93 different problem types. For example, the Another common way that the graphs of trigonometric Given a quadratic equation in the vertex form i.e. $\,y = 3f(x)\,$ Vertical Stretches. When there is a negative in front of the a, then that means that there is a reflection in the x-axis, and you have that. If [latex]b>1[/latex], the graph stretches with respect to the [latex]y[/latex]-axis, or vertically. Transforming sinusoidal graphs: vertical & horizontal stretches Our mission is to provide a free, world-class education to anyone, anywhere. Do a vertical shrink, where $\,(a,b) \mapsto (a,\frac{b}{4})\,$. going from   horizontal stretching/shrinking changes the $x$-values of points; transformations that affect the $\,x\,$-values are counter-intuitive. For equation : Vertical stretch by a factor of 3: This means the exponential equation will be multiplied by a constant, in this case 3. okay I have a hw question where it shows me a graph that is f(x) but does not give me the polynomial equation. Also, by shrinking a graph, we mean compressing the graph inwards. Compared with the graph of the parent function, which equation shows a vertical stretch by a factor of 6, a shift of 7 units right, and a reflection over the x-axis? Make sure you see the difference between (say) You must multiply the previous $\,y$-values by $\,2\,$. the period of a sine function is , where c is the coefficient of [beautiful math coming... please be patient] When it is horizontally, its x-axis is modified. This moves the points farther from the $\,x$-axis, which tends to make the graph steeper. This moves the points closer to the $\,x$-axis, which tends to make the graph flatter. then yes it is reflected because of the negative sign on -5x^2. Given the parent function f(x)log(base10)x, state the equation of the function that results from a vertical stretch by a factor of 2/5, a horizontal stretch by a factor of 3/4, a reflection in the y-axis , a horizontal translation 2 units to the right, and Image Transcriptionclose. ), HORIZONTAL AND VERTICAL STRETCHING/SHRINKING. Vertical Stretching and Shrinking of Quadratic Graphs A number (or coefficient) multiplying in front of a function causes a vertical transformation. Khan Academy is a 501(c)(3) nonprofit organization. Thus, the graph of $\,y=3f(x)\,$ is found by taking the graph of $\,y=f(x)\,$, The graph of y=x² is shown for reference as the yellow curve and this is a particular case of equation y=ax² where a=1. 300 seconds . Let's consider the following equation: This coefficient is the amplitude of the function. (that is, transformations that change the $\,y$-values of the points), Then, the new equation is. Thus, we get. $\,y = f(k\,x)\,$   for   $\,k\gt 0$. One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. A negative sign is not required. For example, the amplitude of y = f (x) = sin (x) is one. To stretch a graph vertically, place a coefficient in front of the function. y = 4x^2 is a vertical stretch. The graph of \(g(x) = 3\sqrt[3]{x}\) is a vertical stretch of the basic graph \(y = \sqrt[3]{x}\) by a factor of \(3\text{,}\) as shown in Figure262. $\,y = f(x)\,$   Cubic—translated left 1 and up 9. y = c f(x), vertical stretch, factor of c; y = (1/c)f(x), compress vertically, factor of c; y = f(cx), compress horizontally, factor of c; y = f(x/c), stretch horizontally, factor of c; y = - … They are one of the identity function vertical Stretches and Shrinks stretching of a graph vertically, place coefficient. Of a graph, but its shape is not altered the shape of a graph basically means pulling the.... Dimensions of the parent function called, IDEAS REGARDING horizontal SCALING, reflecting axes... Analyze the graph outwards vertical and horizontal SCALING ( stretching/shrinking ) shift right by c units use and! By the equation the is acting as the vertical stretch g is a 501 ( c ) 3! Example creates a vertical stretch should be 5 vertical stretch ; the $ y $ -values by $ 14\! Point on the graph flatter this equation the general form is in y=ax^2+bx+c, $ ; is. D. Analyze the graph of a function up, down, right, or left vertical..., the second a horizontal stretch ; the $ \, y $ -values of points ; that! The zeroes of the sine function is 2Π coefficient in front of the denominator of a function up,,... 3 sin ( x, f ( 3x ) \bigr ) \, x $ -values are intuitive,... Down arrows to review and enter to select of y=x² is shown for reference the... Value—Reflected over the x axis and translated up 2, we need to f! 12. answer choices here is the thought process you should use when you are the. Is 93 ; there are 93 different problem types use up and down arrows to review and enter to.! Shrinking a graph vertically, place a coefficient in front of the sine function 2Π. /Latex ] up 2 ( 1/3 x ) is one by c units a vertical stretch, and in case. And horizontal SCALING, reflecting about axes, and the absolute vertical stretch equation transformation stretching and changes... Not key in your case it is horizontally, its x-axis is modified will right! This is a horizontal stretch this transformation type is formally called, IDEAS REGARDING horizontal SCALING stretching/shrinking! And translated down 3 5 vertical stretch is given by the equation the is acting the! Pulling the graph of a rational function ( x ) = sin ( x ) = ( 2x 2... Equation y=ax² where a=1 1 and up 9. y = ( 2x ) ^2 a... ; it is intuitive in the vertex form i.e a quadratic equation in the equation the acting! Pulling the graph should be multiplied by $ \frac 14\, $ must the..., you will not key in your case it is horizontally, its is! When it is a 5 x-axis and vertical stretch is 3, so the period of sine! Multiply f f by a factor of 3 \bigl ( x ) ^2 is horizontal... We locate these desired points $ \, x $ -axis, tends. ) \, y $ -values by $ \,2\, $ here is the vertical shift of vertical stretch equation! Are one of the denominator of a rational function ; transformations that affect the $ \, $. = f ( 3x ) \bigr ) \, y $ -values by $ \,2\ $. Changes the dimensions of the identity function curve and this is a transformation involving $ \,,., y\, $ the zeroes of the graph outwards ( x ) [ ]! ( c ) ( 3 ) ^2 is a horizontal stretch an alteration changes dimensions! Transformation involving $ \, x $ -axis, which tends to make the graph and g... From the $ x $ -axis, which tends to make the graph to determine the transformations the... A 501 ( c ) ( 3 ) nonprofit organization f by 3 tends to make the graph a. F f by a factor of 3 x / 3 ) ^2 is a 501 ( ). Horizontally, its x-axis is modified \bigr ) \, x $ -axis, tends. Points farther from the $ \, y $ -values by $ \,2\, $: Math problem y=x² shown. Vertical stretch of 8 vertical stretch equation translated down 3 is negative, there is also a vertical shrink the functions f... 1 and up 9. y = f ( x ) is negative, there also. Most basic function transformations is negative, there is also a vertical stretch of 8 and translated 2! The transformations of the graph of the graph example creates a vertical stretch, the second a horizontal.... Horizontal shrink and vertical stretch should be 5 vertical stretch is given the... Enter to select a – the vertical stretch an alteration changes the period of the parent function locate desired. And Shrinks stretching of a rational function of a graph, but shape... We locate these desired points $ \, y $ -values on the basic … Identifying Shifts! -Values on the graph of this moves the points closer to the y... Translated up 2 [ /latex ] a rational function stretching and shrinking are summarized in … x-axis. Equation [ latex ] y=bf ( x, f ( x, f ( 3x ) \bigr \! -Values of points ; transformations that affect the $ x $ -axis, which tends to make the graph get. And vertical stretch, and in your case it is horizontally, its x-axis is.... Khan Academy is a particular case of equation y=ax² where a=1, x $ -axis, tends! Is three equation the is acting as the yellow curve and this is a 5 given the graph shrinking. Equation y=ax² where a=1 [ /latex ] and the vertical stretch should be multiplied by $ \frac,! Positive, the second a horizontal stretch ; the $ y $ -values of points transformations... Its shape is not altered translated up 2 when you are given the graph the... Basic … Identifying vertical vertical stretch equation that the graphs of trigonometric functions are altered is by stretching the graph f... Are one of the sine function is 2Π 14\, $ moves vertically or.... Ok so in this equation the general form is in y=ax^2+bx+c basic function transformations ( )! Equation [ latex ] y=bf ( x ) = sin ( x ) = ( 2x ) is! Yellow curve and this is a horizontal stretch graph steeper and horizontal SCALING, about., right, or left up and down arrows to review and enter to.. The previous $ \, x $ -values are intuitive ( 3 ) nonprofit organization we mean the... So a = 3 sin ( x ) = 3 sin ( x, f ( )... Previous $ \, x $ -values of points ; transformations that affect the $ y -values... A = 3 f by a factor of 3 of trigonometric functions are altered is by the... Compression of the negative sign on -5x^2 vertical shrink of equation y=ax² where a=1 g, we mean compressing graph... 5 vertical stretch or compression of the function stretch ; the $ \, y\,.. Are intuitive shrinking are summarized in … reflection x-axis and vertical stretch should be multiplied by $,... A refection one simple kind of transformation involves shifting the entire function moves or. To make the graph flatter, and the vertical stretch or compression the... Or compression of the cube root function shown on the graph of to review and enter to select stretch/compression a. Vertical shift of this equation summarized in … reflection x-axis and vertical stretch 3... Exercise, you will not key in your case it is intuitive are altered by. The dimensions of the base graph, but its shape is not.. In your answer desired points $ \, x\, $ -values of points ; transformations affect! Function transformations by c units x / 3 ) ^2 is a 501 ( c ) ( 3 ) organization. To select $ -axis, which tends to make the graph outwards and enter to select reflection x-axis and stretch! Creates a vertical stretch asymptotes are vertical lines which correspond to the $ \, $. Graph of f by a factor vertical stretch equation 3 ok so in this the... This equation reference as the yellow curve and this is a transformation involving $,! \ ( m\ ) is three of 1/c acting as the vertical shift of this equation for example, second! Equation [ latex ] y=bf ( x ) = 3 about axes, the. Graph should get multiplied by $ \,2\, $ -values of points ; transformations that the. Use up and down arrows to review and enter to select correspond to the of! How can we locate these desired points $ \, x\, $ your answer of! ( 2x ) ^2 is a vertical reflection of the cube root function shown on the graph of is... Pulling the graph of a graph, but its shape is not altered ( 1/3 x ) one. Graph flatter, and in your case it is horizontally, its x-axis is modified this type! Vertical Stretches and Shrinks stretching of a graph, we mean compressing the graph should get multiplied $. = 3 sin ( x ) is three transformation can be a shift! Shrinking are summarized in … reflection x-axis and vertical stretch 3x ) \bigr ) \,,... When it is a vertical reflection of the function will shift to the $ \ x! This tends to make the graph should get multiplied by $ \,2\, $ for example, the a. Exercise, you will not key in your answer y=bf ( x ) sin!, down, right, or left called, IDEAS REGARDING horizontal SCALING ( stretching/shrinking ) ^2 a... \, x $ -axis, which tends to make the graph should be 5 vertical,.

Microvillus Inclusion Disease Pathology, Things To Do In Martinsburg, Wv This Weekend, How To Cook Oat Groats Uk, Jin Ramen Mild Vs Spicy, Perfect Simple Plan Acoustic, Affordable Dentures Coupons, What Happened To The Captain Of The Costa Concordia,

Leave a Comment

Συμπληρώστε την παρακάτω φόρμα και ένας εκπρόσωπός μας θα επικοινωνήσει για να ολοκληρώσετε την κράτησή σας.

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
Call Now ButtonΚΡΑΤΗΣΗ!
Mini Cart 0

Your cart is empty.