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Ymorist [56]
2 years ago
12

How does the graph of g(x) = (x − 2)3 + 7 compare to the parent function f(x) = x3?

Mathematics
2 answers:
sdas [7]2 years ago
6 0

Answer:

Translation 2 units to the right and 7 units up

Step-by-step explanation:

Consider the parent function f(x)=x^3 and the function g(x)=(x-2)^3+7

1. Translate the parent function f(x) two units to the  right. The new function will be

h(x)=(x-2)^3

2. Translate the function h(x) 7 units up, then the translated function will have the expression

g(x)=(x-2)^3+7

Murrr4er [49]2 years ago
5 0

Answer:

First of all, a parent function refers to the simplest function of its type, for example, the parent function of any quadratic function is f(x)=x^{2}.

So, in this case we have a cubic function, which parent function is f(x=x^{3}.

Now, form the parent function we apply specific transformation to get other more complex functions, as the given

g(x)=(x-2)^{3}+7

The transformations applied to the cubic parent function are just translations. The function was move 2 units to the right, and 7 units upwards.

Remember, if we subtract units from the x-variable, the function will move rightwards, if we sum unit to f(x), the function will move upwards.

So, basically these functions can be compared, because they belong to the same family of function, which are cubic, and basically we can get g(x) from f(x) by just applying certain transformations.

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The population of a community is known to increase at a rate proportional to the number of people present at time t. If the popu
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Answer:

P(t) = P(0)e^{0.0693t}

Step-by-step explanation:

The population of a community is known to increase at a rate proportional to the number of people present at time t.

This means that the population growth is modeled by the following differential equation:

\frac{dP(t)}{dt} = rP(t)

Which has the following solution:

P(t) = P(0)e^{rt}

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The population has doubled in 10 years

This means that P(10) = 2P(0). We use this to find r.

P(t) = P(0)e^{rt}

2P(0) = P(0)e^{10r}

e^{10r} = 2

\ln{e^{10r}} = \ln{2}

10r = \ln{2}

r = \frac{\ln{2}}{10}

r = 0.0693

So the equation that will estimate the population of the community in t years is:

P(t) = P(0)e^{0.0693t}

6 0
3 years ago
26 - (2c + 4) = 2(C+6) +C<br> what is c
Zigmanuir [339]

Answer:

c = 2

Step-by-step explanation:

26 - (2c + 4) = 2(c+6) + c

26 - 2c + 4 = 2c + 12 + c

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6 0
3 years ago
Read 2 more answers
It would be amazing if u helped me with the question below, thx! &lt;3
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namely, how many times does 4 x 10⁻³ go into 8 x 10⁶.


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7 0
2 years ago
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Answer:

T= PV/NR

Step-by-step explanation:

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