What transformations are applied to the graph of the function f(x)=10^x to produce the function g(x)=3(10)^x-2

Mathematics

1 answer:

tatiyna3 years ago

7 0

Answer:

D) A vertical dilation by a factor of 3 and a vertical shift down 2 units

Step-by-step explanation:

<u>Given</u>

f(x)=10^x
g(x)=3(10)^x - 2

g(x) = 3f(x) - 2

This is a vertical stretch by a factor of 3 and translation down 2 units

Correct choice is D

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kirill [66]

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3 0

2 years ago

Read 2 more answers

Solve log base 6 (x-6) - log base 6 (x + 4) = 2

Ray Of Light [21]

Answer:

no solutions

Step-by-step explanation:

Since the two terms have the same base, we are able to use the rule for subtracting logarithms:

$log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )$

Therefore, the equation can be written as:

$log_{6}(\frac{x-6}{x+4} )=2$

By using the definition of a logarithm we can say that:

$\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}$

When plugging this solution in, you find that the term $log_{6}(x-6)$ has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so $-\frac{30}{7}$ is not a valid solution. This means that there are no solutions.