Question

Let’s assume that the x

-intercept of the graph of a function p(x)
is 2
. Now:

if q(x)
is a horizontal translation of p(x)
by 3
units to the left, the x
-intercept of the graph of q(x)
is
.
if r(x)
is a horizontal translation of p(x)
by 5
units to the right, the x
-intercept of the graph of r(x)
is
.

Answer 1

-1 and 7.

Explanation:

X-intercept of p(x) = 2.

=> p(x = 2) = 0.

q(x) = translation of p(x) in the - X direction by 3 units.

=> q(x) = p(x -(-3)) = p(x+3).

=>. q(x) = 0, if p(x+3) = 0.

=> if x+3 = 2 => x = -1.

So q(-1) = 0. X-intercept of the graph of q(x) = -1.

Similarly, r(x) = p(x - 5).

r(x) = 0 for x-5 = 2, or x = 7.

So X-intercept of the graph of r(x) is 7.

Answer 2

Answer: q(x)=-1, r(x)=7 - moving left is subtracting from the x-int, and moving right is adding to the x-int. we can find q(x) by doing 2-3=-1. we can find r(x) by doing 2+5=7.