What is the sequence of transformations that will transform $$y=\cos x$$ to $$y=\cos\left(2\left(x+\frac{\pi}{2}\right)\right)+2$$ ?

Halve the period, shift horizontally to the left $$\frac{\pi}{2}$$ units, shift vertically upwards by 2 units.

Halve the period, shift horizontally to the right by 𝜋 units, shift vertically downwards by 2 units.

Double the period, shift horizontally to the left 𝜋 units, shift vertically upwards by 2 units.

Double the period, shift horizontally to the right $$\frac{\pi}{2}$$ units, shift vertically downwards by 2 units.

Halve the period, shift horizontally to the right $$\frac{\pi}{2}$$ units, shift vertically upwards by 2 units.

The function $$y=\log_{10}x$$ is transformed to $$y=3\log_{10}\left[2\left(x+5\right)\right]-4$$ using only four steps. Which of the following is not one of the correct steps to transform $$y=\log_{10}x$$ to the new graph?

Horizontal dilation by a factor of 2

Translate to the left by 5 units

Vertical dilation by a factor of 3

Ch 3 - Graphs and equations

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11th - 12th Grade

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Medium

Grant Rawson

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30 questions

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What is the interval notation for the given number line?

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–6

–33

–107

–216

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Which formula corresponds to the given diagram?

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