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swat32
2 years ago
8

The graph of g(x) is a transformation of the graph of f(x)=3x. Enter the equation for g(x) in the box. G(x) =.

Mathematics
1 answer:
dalvyx [7]2 years ago
8 0

Function transformation involves changing the form of a function

The function g(x) is \mathbf{g(x) = 8(2)^x}

The function is given as:

\mathbf{f(x) = 3^x}

g(x) is an exponential function that passes through points (-2,2) and (-1,4).

An exponential function is represented as:

\mathbf{y = ab^x}

At point (-2,2), we have:

\mathbf{2 = ab^{-2}}

At point (-1,4), we have:

\mathbf{4 = ab^{-1}}

Divide both equations

\mathbf{\frac 42=\frac{ab^{-1}}{ab^{-2}}}

Simplify

\mathbf{2=\frac{b^{-1}}{b^{-2}}}

Apply law of indices

\mathbf{2=b^{-1+2}}

\mathbf{2=b}

Rewrite as:

\mathbf{b =2}

Substitute 2 for b in \mathbf{2 = ab^{-2}}

\mathbf{2 =a(2^{-2})}

This gives

\mathbf{2 =a(\frac 14)}

Multiply both sides by 4

\mathbf{a = 8}

Substitute 8 for (a) and 2 for (b) in \mathbf{y = ab^x}

\mathbf{y = 8(2)^x}

Express as a function

\mathbf{g(x) = 8(2)^x}

Hence, the function g(x) is \mathbf{g(x) = 8(2)^x}

Read more about exponential functions at:

brainly.com/question/11487261

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For the following exercises, find a formula for an exponential function that passes through the two points given. (0,6) and (3,7
kirill [66]

\boxed{\boxed{f(x)=6(5)^x}}

<h2>Explanation:</h2>

An exponential function is given by the following form:

y=ab^x \\ \\ Where: \\ \\ a \ is \ a \ constant \ and \ b \ is \ the \ base

Here we know two points:

(0,6) \ and \ (3,750)

\bullet \ (0,6) \\ \\ x=0, \ y=6 \\ \\ 6=ab^0 \\ \\ \boxed{a=6} \\ \\\ \\ \bullet \ (3,750) \\ \\ x=3, \ y=750 \\ \\ 750=6b^3 \\ \\ b^3=\frac{750}{6} \\ \\ b=\sqrt[3]{125} \\ \\ \boxed{b=5}

Finally, our exponential function is:

\boxed{\boxed{f(x)=6(5)^x}}

<h2>Learn more:</h2>

Behavior of functions: brainly.com/question/12891789

#LearnWithBrainly

5 0
3 years ago
4 a3b(-3a5b3+6a4b)+(3a4b2+6ab)2
Irina18 [472]

Answer:

− 12 a 8 b4+ 24 a7 b 2+ 6a 4b 2 + 12 a b

Step-by-step explanation:

Simplify each term

4 0
3 years ago
A) 24 is what percent of 60
choli [55]

A) 24/60 = 0.4 or 40%

B) 8/x = 4/10 → 20

C) 120 * 0.7 = 84

D) 30/120 = 0.25 or 25%

E) 112/x = 56/100 → 200

F) 128/80 = 1.6 or 160%

G) x/45 = 140/1000 → 63

H) 15/x = 6/100 → 250

7 0
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Andrew spent 75% of his $20 allowance to go to the movies. How much did he spend? Use at least 2 strategies.
earnstyle [38]

Answer:

$15

Step-by-step explanation:

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3 years ago
Please help me with this question
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I don’t know sorry
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