Question

Suppose that the x-intercepts of the graph of y=f(x) are 4 and 6. What are the x-intercepts of y=f(x+5)

Answer 1

An x-intercept has the form \((x,0)\). This means when you plug in this value of \(x\) (the intercept), you have \(f(x)=0\).

So you know that \(f(4)=f(6)=0\).

Answer 2

If the x-intercepts are 4 and 6, then f(x) = (x-4)(x-6)

Answer 3

f(x+5) shifts f(x) to the LEFT by 5 units.
Therefore, the intercepts will shift accordingly (by 5 units to the left).

Answer 4

@Cosmichaotic I don't think we can assume the function is quadratic based solely on two known roots.

Answer 5

Im still very lost. On the back it says the answer is (2,10) and I do not understand how to get that answer.

Answer 6

Have you done translation of function, reflection of function, etc. yet?

Answer 7

We went over it for like 5 minutes.

Answer 8

If f(x) is the parent function, then, for example,
f(x+5) moves the function to the LEFT by 5 units.
f(x-5) moves the function to the RIGHT by 5 units.
f(x) + 5 moves the function UP by 5 units
f(x) - 5 moves the function DOWN by 5 units

Answer 9

That makes sense