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This is the graph for the function f(x) = -x2 + 2. 

a. The graph of f gets multiplied with the factor - 1/2 to create the graph g. How would the graph of function g look like and what would the function notation be?

b. The graph of the function h(x) = 7x2 + b starts from the graph of f by multiplying it with a factor. Calculate the value of b.

 

 Jun 11, 2019
 #1
avatar+669 
+1

a) i'm not really sure what you mean by factor, and function of g, so please be a little more clear and i could answer your question :)
b) a tip would be to imagine this as slope intercept form. How would you find the y intercept of an equation? first you would need to plug a point in and then leave b as a variable and solve for it.
Again, I'm sorry I couldn't give you the answers to this, but if you have further questions or would like to clarify what the question is asking please reply to this, and I will be more than happy to help! :) 
sorry again. 
 

 Jun 11, 2019
 #2
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+1

Oops sorry! English isn't my native tongue so I'm kinda awful at translating the question. Like the graph of f gets multiplied with - 1/2 in/from the x axis and this new graph is the graph for function g. If you still don't understand, don't worry, I already appreciate the intention :)

Guest Jun 11, 2019
edited by Guest  Jun 11, 2019
 #3
avatar+8829 
+2

a.

If you take the graph of  f  and multiply the y-coordinates of every point by  \(\frac12\) , that will vertically compress the graph

 

If you take the graph of  f  and multiply the y-coordinates of every point by  -1 , that will reflect the graph over the x-axis.

 

So the graph of function  g  is the graph of function  f  vertically compressed and reflected over the x-axis.

 

I'm not entirely sure what the function notation is, but I think it is this:

 

g(x)  =  -\(\frac12\) f(x)

 

(Also........I wanted to say "vertically compressed by a factor of  2" or "vertically compressed by a factor of  \(\frac12\) " but I didn't know which is considered correct, and the only thing I could find about this question was here: http://mathforum.org/library/drmath/view/77603.html. It seems like there's not a universally accepted way of stating it, so I just left it out!)

 

b.

f(x)  =  -x2 + 2

h(x)  =  7x2 + b

 

We can see the factor must be  -7  .

 

h(x)  =  -7 f(x)  =  -7( -x2 + 2 )  =  7x2 - 14

 

h(x)  =  7x2 - 14     so we can see that     b = -14

 Jun 11, 2019

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