Complete The Table To Investigate Dilations Of Whi - Gauthmath

July 5, 2024, 1:11 pm

Does the answer help you? Now we will stretch the function in the vertical direction by a scale factor of 3. Complete the table to investigate dilations of exponential functions. Complete the table to investigate dilations of Whi - Gauthmath. By paying attention to the behavior of the key points, we will see that we can quickly infer this information with little other investigation. However, the principles still apply and we can proceed with these problems by referencing certain key points and the effects that these will experience under vertical or horizontal dilations.

Complete The Table To Investigate Dilations Of Exponential Functions Teaching

This is summarized in the plot below, albeit not with the greatest clarity, where the new function is plotted in gold and overlaid over the previous plot. We solved the question! When dilating in the vertical direction, the value of the -intercept, as well as the -coordinate of any turning point, will also be multiplied by the scale factor. Complete the table to investigate dilations of exponential functions in order. This problem has been solved! Thus a star of relative luminosity is five times as luminous as the sun.

The -coordinate of the minimum is unchanged, but the -coordinate has been multiplied by the scale factor. Complete the table to investigate dilations of exponential functions in the table. This result generalizes the earlier results about special points such as intercepts, roots, and turning points. Please check your spam folder. Determine the relative luminosity of the sun? Additionally, the -coordinate of the turning point has also been halved, meaning that the new location is.

Complete The Table To Investigate Dilations Of Exponential Functions In The Table

The roots of the original function were at and, and we can see that the roots of the new function have been multiplied by the scale factor and are found at and respectively. One of the most important graphical representations in astronomy is the Hertzsprung-Russell diagram, or diagram, which plots relative luminosity versus surface temperature in thousands of kelvins (degrees on the Kelvin scale). Geometrically, such transformations can sometimes be fairly intuitive to visualize, although their algebraic interpretation can seem a little counterintuitive, especially when stretching in the horizontal direction. Gauth Tutor Solution. In our final demonstration, we will exhibit the effects of dilation in the horizontal direction by a negative scale factor. Once an expression for a function has been given or obtained, we will often be interested in how this function can be written algebraically when it is subjected to geometric transformations such as rotations, reflections, translations, and dilations. Provide step-by-step explanations. The figure shows the graph of and the point. Complete the table to investigate dilations of exponential functions teaching. In the current year, of customers buy groceries from from L, from and from W. However, each year, A retains of its customers but loses to to and to W. L retains of its customers but loses to and to. This transformation does not affect the classification of turning points. Once again, the roots of this function are unchanged, but the -intercept has been multiplied by a scale factor of and now has the value 4. Answered step-by-step.

Equally, we could have chosen to compress the function by stretching it in the vertical direction by a scale factor of a number between 0 and 1. Other sets by this creator. This makes sense, as it is well-known that a function can be reflected in the horizontal axis by applying the transformation. The function represents a dilation in the vertical direction by a scale factor of, meaning that this is a compression. Suppose that we take any coordinate on the graph of this the new function, which we will label. Stretching a function in the horizontal direction by a scale factor of will give the transformation. This information is summarized in the diagram below, where the original function is plotted in blue and the dilated function is plotted in purple. E. If one star is three times as luminous as another, yet they have the same surface temperature, then the brighter star must have three times the surface area of the dimmer star. If we were to analyze this function, then we would find that the -intercept is unchanged and that the -coordinate of the minimum point is also unaffected. We will now further explore the definition above by stretching the function by a scale factor that is between 0 and 1, and in this case we will choose the scale factor. However, we could deduce that the value of the roots has been halved, with the roots now being at and. Work out the matrix product,, and give an interpretation of the elements of the resulting vector. Given that we are dilating the function in the vertical direction, the -coordinates of any key points will not be affected, and we will give our attention to the -coordinates instead. In many ways, our work so far in this explainer can be summarized with the following result, which describes the effect of a simultaneous dilation in both axes.

Complete The Table To Investigate Dilations Of Exponential Functions In Order

This will halve the value of the -coordinates of the key points, without affecting the -coordinates. The transformation represents a dilation in the horizontal direction by a scale factor of. Coupled with the knowledge of specific information such as the roots, the -intercept, and any maxima or minima, plotting a graph of the function can provide a complete picture of the exact, known behavior as well as a more general, qualitative understanding. As with dilation in the vertical direction, we anticipate that there will be a reflection involved, although this time in the vertical axis instead of the horizontal axis. Since the given scale factor is 2, the transformation is and hence the new function is.

We can see that there is a local maximum of, which is to the left of the vertical axis, and that there is a local minimum to the right of the vertical axis. This means that we can ignore the roots of the function, and instead we will focus on the -intercept of, which appears to be at the point. Referring to the key points in the previous paragraph, these will transform to the following, respectively:,,,, and. Although this does not entirely confirm what we have found, since we cannot be accurate with the turning points on the graph, it certainly looks as though it agrees with our solution. We will use the same function as before to understand dilations in the horizontal direction. And the matrix representing the transition in supermarket loyalty is. At first, working with dilations in the horizontal direction can feel counterintuitive. We could investigate this new function and we would find that the location of the roots is unchanged. Ask a live tutor for help now. The point is a local maximum. In practice, astronomers compare the luminosity of a star with that of the sun and speak of relative luminosity.

As a reminder, we had the quadratic function, the graph of which is below. The plot of the function is given below. Just by looking at the graph, we can see that the function has been stretched in the horizontal direction, which would indicate that the function has been dilated in the horizontal direction. Still have questions? The distance from the roots to the origin has doubled, which means that we have indeed dilated the function in the horizontal direction by a factor of 2. We will choose an arbitrary scale factor of 2 by using the transformation, and our definition implies that we should then plot the function. Get 5 free video unlocks on our app with code GOMOBILE. Note that the temperature scale decreases as we read from left to right. Check Solution in Our App. Create an account to get free access. Suppose that we had decided to stretch the given function by a scale factor of in the vertical direction by using the transformation. Therefore, we have the relationship. We will demonstrate this definition by working with the quadratic. The function is stretched in the horizontal direction by a scale factor of 2.

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