Match each pair of functions to the phrase that best describes the difference between f(x) and g(x). 100 points

See the attachment

A vertical shift adds a constant to the function value. f(x) ⇒ f(x)+5 is a vertical shift up 5 units.

A horizontal shift subtracts a constant from the independent variable value. f(x) ⇒ f(x-5) is a shift right 5 units.

A multiplying factor of magnitude greater than 1 is a vertical expansion; less than 1 represents a vertical compression. f(x) ⇒ -5f(x) is a vertical expansion (and reflection over the x-axis). f(x) ⇒ (1/2)f(x) is a vertical compression.

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Comment on the vertical compression

You have the function f(x) = x² +2 being transformed to g(x) = (1/2)x² +2. If this were a straight vertical compression, the function g(x) would look like ...

... g(x) = (1/2)(x² +2) = (1/2)x² +1

The fact that the constant has remained +2, instead of being enclosed in parentheses or changing to +1, means that the graph has been compressed vertically around the point (0, 2), not the origin.

answer: i could not see part the question so ill explain how to get the answer

step-by-step explanation: for instance the distance she travele d is 10 and she traveled the same amout each mile so do 10 divided by how many miles she drove each time and you ge your answer.

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.