I am confused about using horizontal transformations such as
f(x+a) and f(x-a) to interpret these graphs.
I am confused about using horizontal transformations such as
f(x+a) and f(x-a) to interpret these graphs.
A rule of thumb I use to work out horizontal translations is that the graph moves along the x-axis in the opposite direction to the sign in the function. That is $ \displaystyle f(x+a)$ moves $ \displaystyle a$ units to the left (-ve) and $ \displaystyle f(x-a)$ moves $ \displaystyle a$ units to the right (+ve).
You can verify the direction by plugging values in and seeing what happens. Your example is a cubic so suppose we have the "base" function $ \displaystyle f(x) = x^3$. It is pretty clear that $ \displaystyle f(x) = 0 \text{ when } x = 0$. Now suppose we have $ \displaystyle f(x-4)$ (where a=4). This translation is shifted 4 units to the right according to the previous paragraph and $ \displaystyle f(x-4) = 0 \text{ when } x-4 = 0 \therefore x=4$ which is 4 units to the right of 0.
Let me know if you meant something else
edit: If I take your first example the point (a,b) is to the left of 0 on the x-axis so it'll be which sign inside the function
That doesn't make sense to me. I tried it with a graph in showing the graphs of $ \displaystyle f(x) = -(x+5)^2 \text{ with } g(x) = -x^3$ for comparison and the graph of f(x) is shifted 5 units left compared to g(x).
The first thing you should notice is that when x= a, y= b. Since all of the options have "+ b", the cubic portion must be 0 when x= a so those that have "x+ a" are impossible. That eliminates D and E.
The second thing you should notice is that the usual $ \displaystyle x^3$ is reversed- this graph rises to the left, not the right. That means x is swapped for -x. Since we are using "x- a" instead of x, we must have $ \displaystyle -(x- a)^3$ which is the same as (a- x)^3. That eliminates A leaving B and C which are identical.
Last edited by HallsofIvy; February 2nd, 2014 at 21:14.
so we sub x=a because in the graph it says (a,b)
what if the question said (-a,b) ??