All categories

3 years ago

How does the graph of g(x) = (x - 3)^3 + 4 compare to the parent function f(x)=x^3 ?

Mathematics

2 answers:

masha68 [24]3 years ago

7 0

Answer:

f(x) has moved:

4 units in the positive y direction i.e upwards

3 units in the positive x direction

Step-by-step explanation:

to get g(x), f(x) has undergone the following transformations

f(x) = x³

f1(x) = x³ + 4 (translation of 4 units in the positive y direction i.e upwards)

f2(x) = g(x) = (x-3)³ + 4 (translation of 3 units in the positive x direction i.e towards the right)

Kipish [7]3 years ago

4 0

Answer:

The modified function has a translation of 3 units to the right and 4 units up compared to the parent function.

Step-by-step explanation:

Let's change both functions to y.

How does y = (x - 3)^3 + 4 compare with the parent function y = x^3?

Start with y = (x - 3)^3 + 4 and subtract 4 from both sides.

y - 4= (x - 3)^3

Now compare the function above with the parent function below.

y = x^3

We notice two differences. y of the parent function becomes y - 4 in the modified function. x of the parent function becomes x - 3 in the modified function.

When you replace x by x - h, the function is translated h units horizontally. The translation is to the right if h is positive and to the left if h is negative.

When you replace y by y - k, the function is translated k units vertically. The translation is up if k is positive and down if k is negative.

In the modified function, x became x - 3.

Compare x - 3 with x - h.

h = 3

3 is positive, so the modified function was translated 3 units to the right.

In the modified function, y becomes y - 4.

Compare y - 4 with y - k.

k = 4

4 is positive, so the modified function is translated 4 units up.

Answer:

The modified function has a translation of 3 units to the right and 4 units up compared to the parent function.

You might be interested in

A human’s DNA code, found in nearly all body cells, can be condensed into chromosomes.

Firlakuza [10]

Answer:

I'm a alien, sorry.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Show that if X is a geometric random variable with parameter p, then

Lubov Fominskaja [6]

Answer:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

Step-by-step explanation:

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

$P(X=x)=(1-p)^{x-1} p$

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

In order to find the expected value E(1/X) we need to find this sum:

$E(X)=\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}$

Lets consider the following series:

$\sum_{k=1}^{\infty} b^{k-1}$

And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

$\int_{0}^b \sum_{k=1}^{\infty} r^{k-1}=\sum_{k=1}^{\infty} \int_{0}^b r^{k-1} dt=\sum_{k=1}^{\infty} \frac{b^k}{k}$ (a)

On the last step we assume that $0\leq r\leq b$ and $\sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}$ , then the integral on the left part of equation (a) would be 1. And we have: