Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 3. It comes up from quadrant 4 and increases and curves into quadrant 3. It goes through (2, negative 6), (0, negative 1).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It increases into quadrant 2 and goes through (negative 1, 2) and (negative 2, 6).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2. It increases into quadrant 1 and goes through (1, 2) and (2, 6).

Question

24-07-2022
Mathematics

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Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 3. It comes up from quadrant 4 and increases and curves into quadrant 3. It goes through (2, negative 6), (0, negative 1).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It increases into quadrant 2 and goes through (negative 1, 2) and (negative 2, 6).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2. It increases into quadrant 1 and goes through (1, 2) and (2, 6).

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joaobezerra joaobezerra · Answer 1 · 2022-07-25T21:44:07+02:00

Using translation concepts, the graph that represents a reflection across the x-axis of [tex]g(x) = \frac{3}{4}(3)^x[/tex] is:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A reflection across the x-axis of g(x) means that:

f(x) = -g(x).

g(x) increases from the second quadrant into the first, hence for f(x) it will be from quadrant 3 into quadrant 4.

More can be learned about translation concepts at https://brainly.com/question/4521517

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