On a coordinate plane, 2 exponential functions are shown. f (x) = 5 Superscript x Baseline approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes though (0, 1) and (1, 5). g (x) = 5 Superscript x Baseline + k approaches y = negative 7.5 in quadrant 3 and increases into quadrant 4 going through (0, negative 6) and (1, negative 2). The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k?

−7
−6
5
7

Explanation:

Given

through (0,1) and (1,5)

through (0,-6) and (1,-2)

Required

Determine the value of k if f(x) is translated vertically down

To get the value of k, we perform the following operations.

For (0,-6) --- Substitute 0 for x and -6 for g(x) in

For (1,-2) --- Substitute 1 for x and -2 for g(x) in

To further show that k = -7, we have the following:

When translated downward by 7 units, the function becomes

Recall that: and

So, we have:

Subtract from both sides

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