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3 years ago

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which transformation causes the described change in the graph of the function y = cos x? the transformation results in a horizon

tal shrink. the transformation results in a vertical stretch. the transformation results in a horizontal stretch. the transformation results in a vertical shrink

1 answer:

luda_lava [24]3 years ago

5 0

The transformations that can occur to the graph of the function y = cos x that will exhibit changes would be changes to the angle, or changes to the coefficient. The transformations can be viewed as follows:

y = cos x transforms to y = cos (kx)

k > 1 ; a horizontal shrink occurs
0 < k < 1 ; a horizontal stretch occurs

y = cos x transforms to y = A cos x

|A| > 1 ; a vertical stretch occurs
|A| < 1 ; a vertical shrink occurs

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Step-by-step explanation:

The equation of a circle in the center-radius form is:

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Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

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Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

<u>For the first parenthesis:</u>

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$x^{2}+2(3)x+b^{2}$

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$y^{2}-8y+b^{2}$

We can rewrite this as:

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Hence in this case $b=-3$ and $b^{2}=9$ :

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Then, equation (5) is rewritten as follows:

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<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>

Rearranging:

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At this point we have the circle equation in the center radius form $(x-h)^{2} +(y-k)^{2}=r^{2}$

Hence:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

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