Can you draw different functions that have the same x-intercepts and the same domain and range?

1 answer:

iogann1982 [59]3 years ago

3 0

I'm pretty sure the answer is no. A function looks like this: f(x) = mx + c. Let's add another function, f(y) = ny + d. If the x-intercept is the same, we can subtract c and d from their respective equations. f(x) = mx, f(y) = ny. If the domains are the same, then x and y can have the same value, so we divide it out. f(x) = m, f(y) = n. Finally, if the ranges are the same, the value of f(x) = f(y). So by the substitution property, m=n. Since all the variables equal each other, both functions are equal to f(x) = mx+c! Therefore, they can only be the same function.

Answer: No

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Use linear combination to solve this. It is much faster than substitution. I would start by multiplying the bottom equation by -1.
<span>4x-7y=3
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The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

<h3>What is the dilation of the figure?</h3>

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime. The image of the given problem is attached below. The length of CA is 4.

$CA=4$

The length of a prime is 16.

$AA'=16$

The new dimension will be,

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Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,

$r=\dfrac{20}{4}\\r=5$

This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

Learn more about the dilation of the figure here;

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