The graph of g is a vertical shrink by a factor of 1/3 and a reflection in the y-axis, followed by a translation 3 units right of the graph of f(x)=x2. Write a rule for g.

Transformation involves changing the position of a function.

The rule for g is:

The parent function is given as:

The rule of vertical shrink by a factor of 1/3 is:

So, we have:

The rule of reflection across the y-axis is:

So, we have:

The rule of translation 3 units right is:

So, we have:

Hence, the rule for g is:

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g(x) = (1/3)*(-x)^2 + 3.

Step-by-step explanation:

Let's define all the transformations in a general way,

A vertical contraction/dilation of a scale factor a is written as:

g(x) = a*f(x)

where if a > 1, it is a dilation.

if  0 < a < 1, it is a contraction.

A reflection in the y-axis changes the value of the x-component and leaves the y-component invariable, then this transformation is written as:

g(x) = f(-x).

A translation of A units up (A positive) is written as:

g(x) = f(x) + A.

Then for this case we have:

A dilation with scale factor 1/3.

g(x) = (1/3)*f(x)

A reflection over the y-axis.

g(x) = (1/3)*f(-x)

A translation of 3 units up.

g(x) = (1/3)*f(-x) + 3

(in that order, remember that the order in which you applly the transformations matters)

Then g(x) = (1/3)*f(-x) + 3

and f(x) = x^2, so we can replace that in the equation for g(x)

g(x) = (1/3)*(-x)^2 + 3.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.

answer: 2 answers

step-by-step explanation: the first one means to spread the product throughout the marketplace such that a large number of people can buy it.  

the second means the process of making a product or service available for the consumer or business user that needs it.

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