An exponential function f(x) is reflected across the x-axis to create the function g(x). which is a true statement regarding f(x) and g(x)? 1. the two functions have the same initial value. 2. the two functions will cross each other on the axis. 3. the two functions have reciprocal output values of each other for any given input value. 4. the two functions have opposite output values of each other for any given input value.

(4) the functions will have opposite output values of each other.

Explanation: A reflection across the x axis is achieved by output value inversion: g(x) = -f(x). Therefore the output values will be opposite, by definition of the reflection, at any point x.

NOTE: The answer (2) is also applicable but not in all cases. The functions will cross each other at the x axis, but only IF the function f(x) ever crosses the x axis. This we do not know and so (2) is true only conditionally.

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.

13664

step-by-step explanation:

=cross multiply

=100 x = 13664