Question

Which of the following is the function representing the graph below? graph begins in the third quadrant near the line y equals negative 3 and increases slowly while crossing the ordered pair 0, negative 2. When the graph enters the first quadrant, it begins to increase quickly throughout the graph.

f(x) = 4x
f(x) = 4x − 3
f(x) = 4x + 3
f(x) = 4(x + 3)

Answer 1

f(x) = 4^x -3

Explanation:

All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).

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So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:

f(x) = 4^x -3

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The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.