Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

For the function f(x)= |x+2| -3 , explain the difference between f(2x) and 2f(x). Comparing the y-intercept , x-intercepts

Sagot :

facundo3141592

Answer:

For a function f(x), the y-intercept is the value of f(0), while the x-intercepts are the values of x such that:

f(x) = 0.

Here we can also start with some information about dilations.

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x)

While, again, for a function f(x), an horizontal dilation of scale factor k is written as:

g(x) = f(x/k)

So when here they ask us the difference between f(2x) and 2f(x)

We can say that the first one is a horizontal dilation of scale factor 1/2, while the second is a vertical dilation of scale factor 2.

Now let's analyze the intercepts for each case.

if f(x) = |x + 2| - 3

2*f(x) = 2*(|x + 2| - 3)

        = 2*|x + 2| - 6

The y-intercept is:

2*f(0) = 2*|0 + 2| - 6 = 4 - 6 = -2

and the x-intercepts are given by:

2*f(x) = 0 = 2*|x + 2| - 6

           6 = 2*|x + 2|

         6/2 = |x + 2|

           3 = |x + 2|

Here we have two solutions for x,

x = 1:             3 = |1 + 2| = |3| = 3

x = -5:           3 = |-5 + 2| = |-3| = 3

Now for the other transformation, we have:

f(2*x) = |2*x + 2| - 3

the y-intercept is:

f(2*0) = |2*0 + 2| - 3

         = |2| - 3 = -1

(So the y-intercept is different)

And the x-intercepts are given by:

f(2*x) = 0 =  |2*x + 2| - 3

           3 = |2*x + 2|

           3 = 2*|x + 1|

           3/2 = |x + 1|

Here the two solutions are:

x = 1/2

x = -5/2

So the x-intercepts are also differents.

This happens because in one case, we affect the function horizontally and in the other case vertically, so one could expect that the resulting functions are different (thus, have different intercepts)

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.