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.
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! :)
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 :)
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!)
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