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stira [4]
3 years ago
6

On a coordinate plane, 2 exponential functions are shown. f (x) = 5 Superscript x Baseline approaches y = 0 in quadrant 2 and in

creases 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
Geography
2 answers:
Sveta_85 [38]3 years ago
4 0

Answer:

(A) -7

Explanation:

kiruha [24]3 years ago
3 0

Answer:

k = -7

Explanation:

Given

f(x) = 5^x through (0,1) and (1,5)

g(x) = 5^x + k 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 g(x) = 5^x + k

g(x) = 5^x + k

-6 = 5^0 + k

-6 = 1 + k

k + 1 = -6

k = -6 - 1

k = -7

For (1,-2) --- Substitute 1 for x and -2 for g(x) in g(x) = 5^x + k

g(x) = 5^x + k

-2 = 5^1 + k

-2 = 5 + k

k+5 = -2

k= -2-5

k = -7

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

f(x) = 5^x

When translated downward by 7 units, the function becomes

g(x) = f(x) - 7

Recall that: g(x) = 5^x + k and f(x) = 5^x

So, we have:

5^x + k = 5^x - 7

Subtract 5^x from both sides

5^x - 5^x + k = 5^x - 5^x + 7

k = -7

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