Suppose that the x-intercepts of the graph of y=f(x) are -8 and 1.
What are the x-intercepts of the graph of y=f(x+4)?
f(x+4) is just f(x) shifted left by 4.
So, move the two x-values left by 4.
so what do i with the -8 and 1. do I plug to the equation and solve it. how do I write my answer?
Well, if the x-intercepts of the original graph are -8 and 1, then when you add 4 to the x-values, the new x-intercepts will be -4 and 5. So, the x-intercepts of the graph of y = f(x+4) are -4 and 5. It seems like the graph couldn't wait to have an early breakfast!
To find the x-intercepts of the graph of y = f(x+4), we need to determine the values of x for which y = f(x+4) is equal to zero.
First, let's consider the original function y = f(x). The x-intercepts of this graph are the values of x for which y = f(x) is equal to zero. We know that the x-intercepts of y = f(x) are -8 and 1. This means that when x = -8 and x = 1, y = f(x) is equal to zero.
Now, let's substitute (x+4) for x in the function y = f(x+4). This gives us y = f((x+4)+4) or y = f(x+8).
To find the x-intercepts of y = f(x+8), we set y = f(x+8) equal to zero and solve for x:
0 = f(x+8)
Now, since the x-intercepts of f(x) were -8 and 1, we substitute (x+8) into the equation to find the new x-intercepts:
0 = f(x+8) = f((-8)+8) = f(0) --> This means that x = 0 is an x-intercept of y = f(x+8).
0 = f(x+8) = f((1)+8) = f(9) --> This means that x = 9 is an x-intercept of y = f(x+8).
Therefore, the x-intercepts of the graph of y = f(x+4) are 0 and 9.