Which set of transformations is needed to graph f(x) = -0.1cos(x) - 4 from the parent cosine function? reflection across the y-axis, vertical compression by a factor of 0.1, vertical translation 4 units up

reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

vertical stretching by a factor of 0.1, vertical translation 4 units down, reflection across the y-axis

vertical stretching by a factor of 0.1, vertical translation 4 units up, reflection across the x-axis

The correct option is;

Reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

Step-by-step explanation:

The given function is f(x) = -0.1·cos(x) - 4

The parent cosine function is cos(x)

Therefore, f(x) = -0.1·cos(x) - 4 can be obtained from the parent cosine function as follows;

The negative sign in the function gives a reflection across the x-axis

The 0.1 factor of the cosine function gives a compression of 0.1

The constant -4, gives a vertical translation 4 units down

Therefore, the correct option is a reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer