the first problem:
eqauation of graph as given x(x+6)
replace x by (x+4)
new equation: (x+4)(x+10)
for x = -5 y = -5
do the other problems the same way. The exponential graph is 2^x.
I posted a new thread yesterday which no one has replied to. I simply want to know how to find new points using the information.
Change m(x) to m(x+4) given the following two points:
The arrow indicates that the given points must be changed. In other words, I must find new coordinates using m(x+4).
How is this done?
Please, help me. See picture.
Thanks for your reply but I am still a bit lost. Your said equation but there is no equal sign. If (-5,5) and (0,0) is given, what would be the new points? Can you please do this one for me in full? I can then use your steps as a guide to answer the rest? What about the graph for q(x)? How is that done? Please, see attachment to view q(x). Thank you very much in advanced.
first put negative sign in front of x in the original equation. the answer should be corrected accordingly.
the equation you construct from the graph.
the first graph is a parabola concave downward. then you could write it as -(x-a)(x-b). the negative sign in front of the bracket is because the parabola is concave downward. a and b are the x-intercepts. a=0 from the graph, b=-6 from the graph. that yields the equation of the parabola -x(x+6). now replace x in this equation by x+4 to obtain the new equation. fix x=-5 in the new equation and find y using the new equation.
First look at the attachment.
So for a function such as y=g(x-3)-2, this is a translate of the function y=g(x). What is the translation (a,b)? It's (3,-2); i.e. points on the graph of g are shifted to the right by 3 and down by -2. So if (5,4) is a point on the graph of g,
(8,2) is a point of the translated graph y=g(x-3)-2.
Notice the lack of symmetry in the treatment of x and y coordinates. If the translated equation is y=g(x+a)+b, the corresponding translation is (-a,b). I assume your teacher (or text book) gives some sort of justification for all this.
From the title of your homework, it looks as though you are working toward also scaling the graph of a function. Given y=f(x), the scaled graph has equation y=af(bx). Here the the graph is stretched (shrunk) in the y-direction by the factor a and is stretched (shrunk) in the x-direction by the factor 1/b.
I hope this helps.