The second column shows the left shift of the equation g(x)=log_b(x) when b>1, and notes the following changes: the reflected function is decreasing as x moves from 0 to infinity, the asymptote remains x=0, the x-intercept changes to (-1, 0), the key point changes to (-b, 1), the domain changes to (-infinity, 0), and the range remains (-infinity, infinity). Now that we have worked with each type of translation for the exponential function, we can summarize them to arrive at the general equation for transforming exponential functions.ġ, and notes the following changes: the reflected function is decreasing as x moves from 0 to infinity, the asymptote remains x=0, the x-intercept remains (1, 0), the key point changes to (b^(-1), 1), the domain remains (0, infinity), and the range remains (-infinity, infinity). It does not store any personal data.Summarizing Transformations of the Exponential Function The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. The cookie is used to store the user consent for the cookies in the category "Performance". This cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary". The cookie is used to store the user consent for the cookies in the category "Other. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. The effect of applying a vertical stretch is similar to applying a horizontal compression and the effect of applying a vertical compression is similar to applying a horizontal stretch.To find new key points in a horizontal stretch or compression, multiply the x-values by a compression factor created by using the RECIPROCAL of the number multiplied under the square root sign.Multiplying by a number under the square root sign greater than 1 creates a horizontal compression.Horizontal stretches are created by multiplying the function under the square root sign by a number between 0 and 1.To find new key points, multiply the y-values of the parent function key points by the stretch or compression factor.On the bottom right we have a horizontal shift right. Multiplying the parent by a number between 0 and 1 on the outside of the square root creates a vertical compression. Horizontal Shifts On the bottom left we have a horizontal shift left.Multiplying the parent by a number greater than 1 on the outside of the square root creates a vertical stretch.If a < 0 a < 0, the graph is either stretched or compressed and also reflected about the x x -axis. If 0 < a< 1 0 < a < 1, the graph is compressed by a factor of a a. If a > 1 a > 1, the graph is stretched by a factor of a a. The graph of the square root parent function begins at point (0, 0) and is drawn only in quadrant I since the domain and range of the square root parent function are both greater than or equal to zero. How To: Given a function, graph its vertical stretch.Each x-value is multiplied by the factor to create a horizontal compression of the original graph. The effect of this transformation is to change the shape or curve of the graph by “stretching” it upward or “compressing” it downward.If the factor is greater than 1, a vertical stretch will occur and if the number is between 0 and 1, a vertical compression occurs. The number it is multiplied by is called the factor. At first, working with dilations in the horizontal direction can feel counterintuitive. Since the given scale factor is 1 2, the new function is ( ) 2. A vertical stretch or compression of the square root parent function occurs when the parent function is multiplied by a number in front of the square root. Stretching a function in the vertical direction by a scale factor of will give the transformation ( ) ( ).Some of the key points on the graph of the parent function that are good to know as the graph is transformed are: (0, 0), (1, 1), (4, 2), and (9, 3).The graph of the square root parent function begins at point (0, 0) and is drawn only in quadrant I since both the domain and range of the square root parent are both greater than or equal to zero.
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