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Firdavs [7]
3 years ago
14

How are the functions f(x)=16^x and g(x)=16^(1/2)x related? The output values of g(x) are one-half the output values of f(x) for

the same value of x. The output values of g(x) are one-quarter the output values of f(x) for the same value of x. The output values of g(x) are the square root of the output values of f(x) for the same value of x. The output values of g(x) are the square of the output values of f(x) for the same value of x.
Mathematics
2 answers:
Goshia [24]3 years ago
6 0
F(x) =16ˣ     and   g(x) = 16⁽ˣ/₂⁾

Since 16 = 2⁴, then we can write:

f(x) =2⁽⁴ˣ⁾  and  g(x) = 2⁽⁴ˣ/₂⁾ = 2²ˣ

for x = 1 f(x) =  2⁴ = 16
for x = 1 g(x) = 2² = 4
(√16 = 4)

for x = 2 f(x) =  2⁸ = 256
for x = 2 g(x) = 2⁴ =16
(√256) = 16

for x = 3 f(x) =  2¹² = 4096
for x = 1 g(x) = 2⁶ =  64
(√4096 = 64)

We notice that:
The output values of g(x) are the square root of the output values of f(x) for the same value of x.
 
NeTakaya3 years ago
6 0

Answer:

C is correct on edge

Step-by-step explanation:

I took the test

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Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [x = \frac{-b}{2a}, h(\frac{-b}{2a})].

<h3>Use the equation:  [x = \frac{-b}{2a}, h(\frac{-b}{2a})]</h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

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x = \frac{-8}{2(1)}

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h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

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h(0) = (0)² + 8(0) + 15

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a^{2}+2ab+b^{2}

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