Question

The graph below shows f(x), which represents a parent function, and g(x), which represents a translation of that function. Which statements about the function are true? Check all that apply.

Answer 1

1. f(x)=(1/2)^x

4. The domains of both functions are the same.

5. The translation from f(x) to g(x) is right 4 units and down 2 units.

Answer 2

see below

Explanation:

The graph is apparently exponential with a base less than 1 (decay, not growth). The answer choices suggest the parent function is ...

f(x) = (1/2)^x

A check of a couple of points verifies this is true.

f(-4) = (1/2)^(-4) = 2^4 = 16

f(-3) = (1/2)^)(-3) = 2^3 = 8

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The grid on the graph is spaced 2 units per square vertically and 1 unit per square horizontally. Looking at the topmost two points on the curves, we see the g(x) curve is 4 units to the right and 2 units down from f(x).

The way the curve is translated algebraically is to make g(x) = f(x -4) -2. This means that ...

g(x) = (1/2)^(x -4) -2 . . . . . . does not match an answer choice

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The domain of any exponential is all real numbers, so f(x) and g(x) have the same domain.

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The range of f(x) is (0, ∞), but that of g(x) is (-2, ∞), so the ranges are different.